Almost two centuries before us, Percy Bysshe Shelley came to Este and stayed in the villa as the guest of its incumbent at the time, Lord Byron, and in October 1818 was moved to pen his Lines Written Among the Euganean Hills, reflecting his state of mind following the death of his young daughter, Clara, in Venice the previous month.

Having trod some 11 miles in the kind of heat in which we don't normally walk, we're particularly savouring a bench, strategically placed in front of the gates of the villa, which is closed and swathed in the scaffolding of restoration. We are deluged with late afternoon bird song – rather, we like to think, as the troubled poet may have been. "Many flowering islands lie/In the waters of wide Agony," the poem continues, and the Euganean Hills which seem to have granted him some respite from grief were themselves once volcanic islands in a prehistoric sea. Today they rise sharply from the plains of the Veneto, conical and furred with woodland. Think of the Eildon Hills, except more of them, and lushly clad with woods of oak, pine and chestnut, terraced with vines and olives.

Two minutes down the road from the Villa de Kunkler and we're into our hotel, the Beatrice d'Este, where a beer on the terrace proves very welcome, a lizard eyeing us from a window box of geraniums, curved in the sunlight like a small, bronze talisman. We're exploring the Colli Euganei by way of a self-guided, hotel-to-hotel walking tour, organised by Headwater Holidays, and walking (especially when the bulk of your luggage is delivered to your next hotel) is an ideal way to discover this beautiful area.

"We don't start looking for you unless you don't arrive by 7pm," the Headwater rep, Sarah, had assured us at an informal briefing after she'd picked us up, plus half a dozen other walkers and cyclists, at Vicenza station and driven us to our first night's accommodation. We'd flown from Edinburgh to Venice Marco Polo airport, via Heathrow, before catching the train from Venice Mestre. In truth, apart from the heat on some days (others proved damper and cooler) it was straightforward enough walking and we were sometimes ensconced in our destination hotel by mid-afternoon. In the evenings, we'd meet up with other Headwater hoofers, comparing convivial notes on not seeing the wild boars we'd been warned about, and so forth.

The hills first came into sight as Sarah drove us out of Vicenza, rearing darkly from the surrounding plain, an area settled and cultivated since time out of mind, initially by the distant people known as the Paleoveneti, for whom Este, some 36 miles inland from Venice, was a stronghold. Myriad churches and fortresses sprang up during the Middle Ages – elegant bell towers still rising amid the trees and pantiled roofscapes.

Wandering through sleepy villages in the middle of the day, we'd find the streets deserted and shutters drawn, everyone presumably resting or sensibly staying in the shade. Occasionally, someone might give us a bemused "Buona sera" over a fence, doubtless thinking in terms of mad dogs and Englishmen, for Italians, it seems, don't "do" walking, although, boy, do they cycle – but of that, more later.

Following Headwater's detailed route instructions, we only really got ourselves temporarily lost twice, resolving things satisfactorily on both occasions. The second glitch, during the 13-mile final stretch (we lengthened it by climbing to a ruined hilltop monastery, magnificent views making it well worth the detour) had been made, at the same spot, by at least two other couples, and Sarah agreed to revisit it and perhaps re-assess the directions.

Our hotels were a nicely varied bunch, starting with Il Feudo outside Cortelà, an agriturismo in a substantial old farmhouse with chimneys that would have warmed the heart of Gaudi. The place has been in the same family for two centuries and produces its own wine, honey and olive oil. When, to accompany our gnocchi with cheese and glistening guineafowl, they offered us the house wine, they meant it.

Walking from Il Feudo to Este on our first day, and gaining height, we started to feel as if we were peregrinating through some Renaissance canvas, the surrounding terraced slopes, with their bell towers and cypress pinnacles, looking as if they might form the backdrop to some messy martyrdom or fleshy Bacchanal. Along sunlit paths, lizards skittered out of our way and crickets bounced about the foliage.

Este we found an engaging little town, with its arcaded streets, its main thoroughfare crammed with a market the morning we explored it, stalls banked up with glistening fruit and vegetables, while the town's imposing old clock gazed down in inscrutable munificence, its big blue face adorned with stars and the revolving phases of the moon. At least it's still vertical: a few blocks away teetered the 12th-century campanile of San Martino, the most spectacularly off-perpendicular edifice I've ever seen.

Well worth a visit is Este's Museo Nationale Atestino, which provides an extensive insight into the many layers of human habitation that have accumulated here. But make sure you look up from the artefacts from time to time, to appreciate the wonderful trompe-l'oeil frescoed ceilings.

Under the ponderous vault of St Tecla's, the town's duomo, which we visited primarily to view its dramatic altar painting by Tiepolo, we found ourselves contemplating what we were assured was the "uncorrupted body of the Blessed Beatrice d'Este", one-time renowned beauty then ascetic holy woman, who died in 1226. Uncorrupted she might well be, but prepossessing she ain't, as her preserved visage leers toothily out from under an ornate glass case.

They seem to like mummifying things here. Next morning found us in the steep, cobbled hill village of Arqua Petrarcha, named after Francesco Petrarch, the 14th-century scholar, poet and father of humanism – some argue father of the Renaissance itself. We visited his house, where he wrote in 1371, "In the Euganean Hills I had a small house built, seemly and noble; here, I live out the last years of my life peacefully, recalling and embracing with constant memory my absent or deceased friends." At least one of his friends remains, in the shape of what is traditionally regarded as his mummified cat, still guarding the premises, perhaps against paranormal mice. Gazing at the view from his rooms – decorated after his death with frescoes illustrating his life and works – we sense again that timelessness, as the landscape falls away from the village, terraced and cultivated and surely not too different from how it must have been in Petrarch's day.

And so we tramped on, descending into the village of Valsanzibio amid a swarm of tiny frogs, as the place welcomed us with after-rain birdsong and barking dogs. We visited its famous gardens, an extravagant – if, on a damp day slightly gloomy – example of Italian Baroque landscaping, with its high hedges, grottos and statuary and its long perspectives of ponds and fountains guiding the eye up to the elaborate frontage of the Villa Barbarigo.

From there we continued to Galzignano and the warmly welcoming Hotel Belvedere, where our little ground-floor balcony was framed with luxuriant jasmine, its scent permeating the room. Galzignano itself was a pleasantly workaday little town, its two hardware stores overflowing with everything from straw-wrapped glass flagons for olive oil to power saws, reflecting local industries. In its cheerful café, our aperitifs, a Prosecco and a spritzer, cost us a princely t3 – something of a contrast to the tariffs of Venice, a mere half-hour's drive away.

Heading out from Galzignano, we passed below an ancient monastery (no women visitors allowed), the clamour of its bell drifting down through the woods. Eventually a wonderful strada bianca wound its way down under the towering Rocca Pendice, a rock outcrop popular with climbers, and into the little hill village of Teolo, where the beautiful and hospitable Hotel Villa Lussana awaited us. From our balcony in this Liberty-styled villa, built in 1900, the views were simply breathtaking, with glimpses of the Venetian plain beyond waves of dark green hills. On a clear winter's day, the proprietor told us, he can see the lagoon of Venice.

The next morning we awoke to the sound of church bells, and the chatter of massed cyclists milling about in the street below. Lean ciclistas were converging on the lion's head fountain set into the wall below the hotel, like bees to a honeypot, insectoid in their wrap-round shades. As they filled their water bottles, motorcyclists were also gathering, the two factions, lycra and leather, interweaving alarmingly but seemingly without accident. Elsewhere, we'd seen the pedallers in less vocal mode, straining grimly up the steep gradients and hairpin bends of the Euganean roads.

We stuck to hoofing it. During a day out from the Lussana, we took a short walk round the nearby Monte Grande – a popular one, by Italian standards, which meant we met a handful of people, some on horseback. Descending from its sweet chestnut woods, which have provided the region with food, fuel and tannins for dyeing over millennia, our path passed the tiny chapel of San Antonio, set amid a rocky landscape where yellow-flowered cacti, oak saplings and abundant wildflowers flourish side by side. In the official guide brochure for the Euganean Hills Regional Park, a translator with florid tendencies noted that the area's geology and microclimate were "artificers of great floristic exuberance". He wasn't so far off the mark.

FACTFILE

PACKAGE

Jim Gilchrist walked in the Euganean Hills with Headwater, flying with British Midland from Edinburgh to Venice Marco Polo airport via Heathrow. Tel: 08700 662650 or visit www.headwater.com

n An eight-day walking tour, including flights, costs from £919 per head for departures until 8 September. Headwater can arrange flights from most UK airports, with connecting transfers. Prices cover, as standard, return BMI flights from Heathrow to Venice Marco Polo, rail transfer from Venice Mestre stration to Vicenza, plus the 40-minute transfer to the first hotel by minibus. For travel by first-class rail, add £8 per person.

AND THERE'S MORE

For further information on the Euganean Hills Regional Park visit www.parchiveneto.it/ eng/parco-regionale- colli-euganei.php

For alternative walking tours, visit www.holidays.scotsman.com