Žanjic is across the strait on the Luštica peninsula and counts as the best swimming beach within easy reach of Herceg Novi. The pebbles are unusually white and round, the water is clear, and the olive groves come right down to the shore. There's a small restaurant and parasols for rent.
The simplest way to get there is the small boats that leave the Herceg Novi promenade through summer — about 30 minutes each way, with stops at the Blue Cave on the way. By car it's a longer trip around the bay via Tivat and the Verige strait.