Tivat is a town in Coastal region of Montenegro, located in the Bay of Kotor. As of 2011, its population was 9,367. Tivat is the centre of Tiv…Tivat is a town in Coastal region of Montenegro, located in the Bay of Kotor. As of 2011, its population was 9,367. Tivat is the centre of Tivat Municipality, which is the smallest municipality by area in Montenegro.