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Once, its Adriatic shores meant holidays for apparatchiks and a base for the Yugoslav navy. But over the past few years, Montenegro has gone upmarket so rapidly that Cannes and Capri are looking over their suntanned shoulders. The palms may be imported, but the clear seas are real. And it’s half the price of the rest of the Med.

With a classic Mediterranean climate, long days of sunshine are virtually guaranteed, and best enjoyed lounging by its postcard-perfect lakes and beaches.

The towering Montenegrin mountains, mellow harbour towns and sleepy fishing villages fringe this long coastline — with quayside restaurants serving hearty meat and fish stews, spicy sausage and smoked hams, washed down with tasty wines from vineyards in the southern and coastal regions — local grape varieties include vranac and krstac. Catch one of the open-air festivals which take place in summer holiday destinations throughout the season.

Main photo: Sveti Stefan beach (Getty Images)

Water babies can swim through the iridescent waves of Montenegro’s greatest natural wonder, the Blue Grotto, also known as the Blue Cave. It’s so colourfully gorgeous that some first-timers assume there must be lights down there on the seabed. For more seaside fun, visit Petrovac, an idyllic horseshoe bay 12 miles south of Budva. While indolent snoozers occupy the loungers on the main public beach, take your pick from the ice-cream stalls on the promenade. If it’s all too busy, amble over the headland to Lucice beach: less accessible, it’s always refreshingly quieter.

For more outdoor adventures, escape to the mountains and go white-water rafting along the inky-black Tara River in Durmitor National Park. Or try Lake Skadar, the largest lake in the Balkans, which is shared with Albania.

More than worthy of its Unesco world heritage listing, Kotor has cobbled streets, Venetian-built buildings and medieval squares, plus a fascinating maritime museum. In this pocket-sized Dubrovnik, a shrine to its patron saint, Tryphon, drips with more silver and gold than Liz Taylor on Oscars night. You’ll find it upstairs in the Romanesque cathedral on St Tryphon Square. Afterwards, sneak out to the balcony in front of the cathedral’s rose window. It’s a secret place beyond the crowds, perfect for writing postcards. Kotor’s breed of long, thin cat is the unofficial symbol of the town — ask why and you’ll be told about the many ships’ cats who found a retirement home here in past years.

Budva has medieval walls and a riviera coastline indented by small coves and shingly beaches. Visit its stately library with model galleons, busts of Roman emperors and leather armchairs where you can settle in for a breather. While you’re here, take in the pantile panoramas over the town, and the vertiginous mountains of Montenegro beyond — and take a boat to the island of Sveti Nikola, known locally as “Hawaii”.

Stari Bar’s muscular Byzantine fortress broods over Bar’s ruined old town like a Helm’s Deep from The Lord of the Rings — squint and you’ll think that’s Viggo Mortensen preparing to repel invaders from Tolkien’s fantasy stronghold. The Venetians and Turks fought over this castle — you can tell as much from the Lion of Venice statue as you enter, and the expertly restored Ottoman hammam inside.

One final unmissable sight is the pearly white Ostrog Monastery. Tucked into a cliff face almost 900m above the Zeta valley, it’s the most important site in the country for Orthodox Christians and attracts around a million visitors every year.

The sprawling, misshapen Bay of Kotor is home to some of Montenegro’s swishest and most luxurious hotels, notably the Regent Porto Montenegro near Tivat, which looks out over the country’s only superyacht marina. On the other side of the bay is Europe’s sole outpost of the swanky One&Only chain, the Portonovi. Head out of the Bay of Kotor into the Adriatic and veer to the east, where the Chedi Lustica Bay forms one of the central parts of the smart development overlooking Lustica Bay.

Carry on further south towards Petrovac and you can choose from a huge range of hotels, villas and apartments. The beachfront Hotel Riva has one of the most enviable positions in the town. Active types can base themselves in the northern town of Kolasin for skiing or hiking in Biogradska Gora and Durmitor, while keen kayakers can stay in or around Virpazar on Lake Skadar.

For some of the finest views of Kotor and the bay beyond, follow the madly zigzagging trail to the medieval fortress of St John, which stands high over the old town. Known as the Ladder of Kotor, the steep footpath takes you along at least 70 dizzying switchbacks, with the views getting more and more stupendous as you get closer to the top. It’s at least a three-hour hike — longer if you can’t resist stopping to snap all those knockout vistas.