Having had our fill of brownfields, we journeyed further inland. On the other side of the fjord is Kotor Bay, a UNESCO World Heritage Site with plenty of pretty waterfront towns set against a backdrop of jagged cliffs. It's part alpine lake, part playground of the erstwhile Venetian Republic. The best way around the bay is by speedboat and it is easy to find a local pot-bellied captain to take you out for an afternoon spin for 50. Our first stop was the beautifully restored 15th-century hamlet of Perast. While Dragan, our skipper, smoked a cigarette, we explored the winding stone corridors and intricate façades of the local townhouses, one of which belongs to Michael Douglas and Catherine Zeta Jones. Pamela Anderson also has a spa hotel in the offing nearby, and Jay Z and Beyoncé rocked up in a yacht last summer, sending a wave of excitement around the bay, eclipsing interest in gas, fertiliser and steel-pipe billionaire Andrey Melnichenko, who had dropped anchor in his Philippe Starck-designed yacht, A, named after his model wife Aleksandra, a cover girl for Russian Tatler.