Kotor Bay, which is on the Unesco World Heritage list, is a dramatically beautiful inlet where fishing settlements such as Prcanj cling to steep escarpments, the red roofs of squat houses bright in the sun. Squint, and the whole picture is like a glorious marriage between the fjords of northern Europe and a more rustic version of the Italian Lakes.

Until recently, the easiest way to reach Kotor Bay was via a 90-minute drive from the Croatian city of Dubrovnik and its international airport – an inconvenient transfer which means that, to some extent, the area has remained a secret for those in the know.

But now Montenegro Airlines has launched a direct flight from Gatwick to Tivat and holidaymakers are starting to explore this dramatic landscape.
Not just any holidaymakers either.

Chelsea FC supremo Roman Abramovich has discovered Montenegro as a destination – and former James Bond Pierce Brosnan was in Tivat a couple of weeks before my visit.

Abramovich was lured to the Balkans by Porto Montenegro – an exclusive option (in Tivat) for those with boats. It is one of the largest marinas on the Adriatic, with 245 berths.

It is also one of the few docking enclaves on European waters that can cope with the super-yachts favoured by the likes of the Russian billionaire. The world’s top-ranked male tennis player Novak Djokovic and onetime Formula One team owner Eddie Jordan have also been seen mooring up here.
Not so long ago, Porto Montenegro was a naval shipyard in the old Yugoslavia.

It has changed radically. There are some 40 swish shops and five smart restaurants – including the country’s first sushi joint, the lively Mitsu. In truth, the development feels rather at odds with the rest of the more prosaic town of Tivat, which is home to about 20,000 souls. But the district around the port is showing signs of gentrification with new bars and eateries – such as Prova – opening up.

Nearby, the Purobeach chain – which specialises in ultra-chic swimming pools with bars and clubs attached – has also arrived in town. Its 215ft-long infinity pool – outrageously cantilevered over the sea – and surrounding set-up has just been voted the ninth best beach bar in the world. Financier Nat Rothschild hosted his star-studded 40th birthday party here at a reported cost of £1million.

I stayed at the Primavera Lux hotel on the front – a well-run, old fashioned establishment with a robust local menu of fish, meats and soups. But what the port – and indeed, the whole area – needs is a better selection of hotels to look after the starry clientele.

The boutique Hippocampus hotel, in the walled town of Kotor (at the end of Kotor Bay) opened last summer, and a five-star Regent opens next summer in Porto Montenegro. Across the water, another former military site has just been unveiled – as the Lustica Bay resort begins to take shape.
At the moment, there is a golf driving range, an archery centre and a cool beach bar, Almara.

But soon, Lustica Bay – backed by Orascom, the company which carved the community of El Gouna out of the desert in Egypt – will boast up to seven more top hotels and a wellness spa as it attempts to create a whole new town, as well as a harbour, from scratch. There will be two marinas with 170 berths, and more than 1,500 homes.

It is an ambitious project that will stretch over 17,000 acres of hilly terrain between the inland waterway and four miles of the Adriatic coast. It will offer incredible views in every direction, as well as a championship golf course – the first in the country.

For now, any visit to Kotor Bay should include as much time as possible on the water – all the locals have a little vessel for trips to the shops.
A trip on the Coche D’Eau boat is a very popular – and cheap at €12 for an eight-hour jaunt. It takes you around the Bay, leaving Tivat every morning, and taking in sights such as Our Lady of the Rocks, a stunning church that perches on a rocky islet in the middle of the water.

Montenegro – a country without a single McDonald’s or Starbucks – is ripe for exploration, even before Lustica Bay and other new developments are up and running.

And with the national team just as likely as England to be playing at the World Cup in 2014, Montenegro’s emergence as footballing power could be matched by its promotion to the premier league of tourist destinations.