“We drove to Sveti Stefan, stayed in a B&B, and told Nada, the owner, that we were depressed because we couldn’t find somewhere nice. She and her daughter, who spoke a bit of English, went off and found a local builder, who was completing a small apartment block. Nada found us a lawyer and we went to court in Cetinje (the former capital) with her daughter on the day we were flying back, spoke to the magistrate, signed all the documents and then, very scarily, transferred the money to the builder.”

Hensman and Rossiter rent out their flats for £250-£530 a week. They were lucky: the usual advice to buyers is to use a reputable estate agent and ask them to recommend a good lawyer. Be prepared to move fast and open a local bank account so that your deposit, usually 10%, can be handed over straight away. Sellers are rarely willing to wait more than two or three days for it. Once the deposit is paid and pre-contract documents signed, both sides are committed and face heavy financial penalties if they pull out.

Other expenses include 2% stamp duty, the estate agent’s commission of 2%-5% (usually paid by the buyer) and legal fees of £300-£700. Mortgages on Montenegrin properties are not yet available, though two Austrian banks are expected to enter the market soon. Most Britons intending to buy there either remortgage at home or use their savings.

British buyers also need to be aware that to own land (the definition of “land” varies from one area to the next, but usually applies to anything beyond a small house with garden), they must set up a company for the purchase. And stick to the rules — Milan Bigovic, a property consultant, says: “British buyers sometimes think this is a cowboy land and ignore the right procedures. We have a client who faces a €250,000 (£170,000) penalty for failing to transfer his money correctly.”

Two-bedroom flats in the old towns of Kotor or Budva, a lively resort near Sveti Stefan, typically cost about £100,000. A ruined Montenegrin stone house, ripe for renovation, will cost anything from £30,000 to £500,000, depending on how close to the sea it is.

One agency, Someplace Else, recently sold its first property near the Tara Canyon, said to be the deepest in the world after the Grand Canyon in America.

But if the scenery is beautiful and the buying process fast, the country itself still poses problems. The road round Kotor bay is narrow and rutted and can be a hair-raising drive. Water and electricity supplies can be unreliable in summer, while telephone and internet connections are often ropy. Check, too, that the home you want to buy has its own cistern.

Your lawyer will also need to check whether new developments are likely to spoil your sea view or rural seclusion. The Lustica peninsula between Kotor and Budva, criss-crossed by dry-stone walls, overgrown olive plantations and deserted villages, for example, offers bargains but may yet see an explosion of concrete.

As Andrea Marston, of Dream Property Montenegro, says: “It’s all part of the charm, but Montenegro’s definitely a rough diamond.”

On the market

Fourteen miles from Kotor and a mile from the nearest neighbour, this seven-bedroom house, in 0.6 acres within Njegusi national park, is for sale for £245,000. Total Group, 00 381 6944 4895, www.totalgroup.org

A stone cottage by the sea on Kotor bay, this two-bedroom home comes with two moorings and two small boats. It is £204,000 with Dream Property Montenegro, 01753 831 182, www.dreammontenegro.com

For sale for £31,000 in Marovici, Lustica, this farmhouse, which comes with an old olive press, could be converted for £40,000. Dream Property Montenegro, 01753 831 182, www.dreammontenegro.com

By the sea in Herceg Novi, this £200,000 house is split into three flats. Two have balconies, one, a garden; they would let as holiday homes. Montenegro Living, 00 381 8835 0485, www.montenegro-living.com

Times recommends

• Second homes: credit crunch casualty or money-spinner?
• How I built my own sliding house
• Top 10 incentives for house buyers