Kostanjica, Montenegro offers 1 beach perfect for sunbathing, surfing, swimming, and more. Kostanjica, Herceg Novi, Montenegro, is known for its picturesque views of the Bay of Kotor and its proximity to the historic town of Perast. The best time to travel to Kostanjica, Montenegro, is from June to September, when the average air temperature is around 25°C (77°F) and the water temperature is approximately 23°C (73°F). Sandee provides detailed maps, photos, and reviews from fellow beachgoers to help you Choose Your Beach™ and plan your perfect beach vacation!