Lunching in the old town at Kotor, we overhear a crusty salt of the sea regaling his companions about "sailing into Kos harbour in 1967".

I fail to catch what happened on Kos back then, but we distinctly hear the man's wife inquire of the waiter, "Why the dickens, with all those mountains, would Montenegro experience water shortages?"

The water supply has indeed been cut, a common occurrence along this coast in summer, but the waiter is flummoxed. An uncomfortable silence ensues before the woman resorts to speculation. "I expect it's the pipes," she sniffs.

I don't know about the pipes but I can vouch for the mountains. Part of the Dinaric chain that forms the backbone of the Balkan peninsula, they dominate Montenegro's Adriatic coastline for most of its 293 craggy kilometres. Usually the mountains stand back, frowning down upon walled towns, pine-clad coves, crumbling castles and medieval monasteries tucked away among foothills quilted with olive, citrus and pomegranate.

However, at the Boka Kotorska, or Bay of Kotor, the limestone muscles in. Vast cliffs steeple upwards from a brooding expanse of water composed of four bays connected by narrow channels, creating what is usually called Europe's southernmost fjord.

We arrive during a thunderstorm, careering around the Boka shores in a badly driven taxi. Black clouds smother the mountaintops. The driver's patter about beautiful beaches and cheap restaurants goes unheeded as a sudden gale tramples the sea, tossing wooden dinghies at their moorings and unleashing waves against shingle coves framed by willows.

Across a misty distance, Italianate campaniles crown wooded promontories; walled villas peek from shrouds of jasmine and bougainvillea. Appearing at the head of the Boka, crouched behind ramparts that are twice the length of Dubrovnik's, the old town of Kotor possesses the blurred quality of a watercolour.

The situation looks ripe for drama. So it's no surprise to learn that UNESCO-listed Kotor, founded originally by the Romans as Acruvium, has been much coveted and repeatedly fought over.

Its architectural character stems from a period of Venetian rule from 1420 to 1797, when, owing to its position on the Ragusa-Constantinople trade route and the aptitude of its merchants and mariners for seaborne commerce, the town became extraordinarily wealthy.

Profits went into real estate, with palazzos and townhouses springing up on a tangle of lanes that, it must be said, give the impression of having been laid out at the whim of a drunken sailor.

Consequently, Kotor favours an idling approach. This we attempt, crossing the Skurda rivulet on a wooden footbridge and entering the town through its northern gate, erected in 1540 to celebrate the repulse of a siege by the notorious corsair Khair ed-din Barbarossa. Inside the gate on a rain-washed piazza, the 14th-century Church of St Mary, all pink and white stone, looks freshly minted. As locals unfurl washing from upper windows to catch the returning sun, we plunge among alleys framed by buildings of textured stone, with ornate balustrades and neat rows of timber-shuttered windows.

Eventually, Jo announces that we are going in circles. It hardly seems to matter. We stroll down lanes redolent with cooking smells, observe weathered escutcheons and battered buskers, and, bypassing the inevitable galleries and boutiques, follow vaulted passageways into courtyards where siege-defying cisterns, bronze spigots with the heads of lions or dragons and rusty anchors, casually discarded, recall a swashbuckling past.

Punctuating the maze with satisfying regularity are more piazzas, most with a medieval church in the centre and restaurant and cafe tables scattered around the perimeter.

Taking advantage of this arrangement, we follow our tour of the 12th-century Cathedral of St Tryphon with a pizza of wind-cured Njegusi ham at La Pasteria, an Italian eatery located opposite. Sipping vranac, Montenegro's palatable purple wine, we watch darkness fall and spotlights illuminate the cathedral's Romanesque facade with its twin campaniles of pale Korcula stone, the latter baroque footnotes added during reconstruction following an earthquake in 1667.

Next morning, when the arrival of a cruise ship fills the alleys with daytrippers, we flee to the Maritime museum. Arranged throughout the Grgurina Palace, a fascinating collection of nautical paraphernalia documents a seafaring tradition dating to the 9th century. The subsequent appearance of another liner prompts a more extreme course: we climb the Fortress of St Ivan, an airy wilderness of thistles, cypresses and sunburnt grass whose uppermost bastion, 260m above the sea, lies atop 1350 occasionally dodgy steps.

Things become hectic when Jo, inspired by a view of rooftops, sea and mountains that grows more emphatic with each painful step, begins to run. At the top I experience a mild psychosis induced, I suspect, as much by lack of oxygen to the brain as by the stunning vistas. As a timely breeze cools the sweat on our flesh, we watch clouds drag shadows across the surface of the Boka and over ranks of tobacco-coloured mountains leading towards Bosnia and Herzegovina.

The discovery of an obscure postern encourages an alternative descent. We follow a trail past an abandoned hamlet to the old Ladder of Kotor, a venerable mule-track that zigzags spectacularly up the face of the Lovcen massif. Before the road was constructed in 1879, and while foreign powers controlled the coast, this track provided the only way into Montenegro, back then a remote, mountain-girt republic known for its ornery inhabitants.

Once trodden by diplomats, merchants, spies and the odd intrepid traveller, today the Ladder retains its transitional role, linking the tourist-friendly coast with the wild and less-visited interior.

Thus inspired, we broaden our horizons. Westward lies Prcanj, a former sea captain's bolthole with a gargantuan church containing paintings by Italian masters, Tiepolo among them, and a silver cup once owned by Lord Byron. Trundling uphill through a forest of oak, horse-chestnut, laurel and juniper, we locate a pair of abandoned churches, antediluvian shells propped in sunny glades peppered with autumn wildflowers. In the hot stillness we sense a presence, which proves to be a slender green snake unwinding itself from a bough.

At sleepy Perast, the palazzos recall a golden age when the town's location astride the two main bays of the inner Boka, opposite the Verige channel, endowed it with considerable strategic consequence.

Perastin sailors were renowned for their bravery, while the town once boasted a nautical academy of renown; when Peter the Great of Russia created his navy, he sent his fledgling admirals here. Perast's lustre has faded but it is worth visiting, if only to hitch a ride with a local boatman to a pair of nearby islets steeped in history.

Our voyage assumes epic proportions as mountains loom like dark towers and sunbeams, piercing formidable clouds, lay shimmering ducats of light on the sea. Cleaving glossy black water, we pass the first outcrop, like an isle of the dead with its cypress-shrouded chapel, and moor at the second which, we learn, is artificial, having been constructed by the Perastins from scuttled ships and stones transported from the mainland by the boatload, reputedly in atonement for the murder of an unpopular prelate perpetrated during mass one Sunday morning in 1535.

Outside the little blue-domed church, dedicated to Our Lady of the Rock, tourists lounge on benches erected after the event for the purposes of arbitration. Stepping inside, we are surprised by the sudden baroque splendour: biblical scenes in oil, a chequerboard floor and a finely sculpted altar of Carrara marble. Beyond the altar a door leads into the former keeper's lodge, now a museum.

Immersed among Greek and Roman amphorae, rusty cutlasses, antique fittings and an ingenious hand-turned screw that once propelled the local boat, we join a group whose fey young leader describes how a local woman occupied herself during her sailor-husband's absence by weaving, Penelope-like, an intricate icon.

"When she ran out of thread she used her hair. And look! It was golden when she began but grey by the time she finished."

"The husband came back?" queries a gruff American.

"No, he never did. Jacinta Kunic died. It is very sad."

Jo rolls her eyes, leaning against the wall in merriment. "What a legend," she says.