Den Ham Castle, locally known as Kasteel Den Ham or Hamtoren was built probably in the 14th century (the lower part of tower and the great hall have survived). In the 19th century the castle was already mainly demolished. The castle has stood empty for quite some years but is now privately inhabited and can thus not be visited.
References:Herceg Novi was founded (on a former small fishing village, existing since Roman Empire times) as a fortress in 1382 by first Bosnian King Stjepan Tvrtko I and was called Sveti Stefan or Castelnuovo. The Turks conquered Herceg Novi in 1482, and ruled for 200 years, until 1687. However, there was a short pause between 1538 and 1539 when it was held by the Spaniards before they were defeated in the Siege of Castelnuovo. Turkey ruled again until 1687, from then until 1797, the town was ruled by the Venetian Republic.
The Herceg Novi old town is amazing. It is on a fairly steep hill that leads all the way down to the sea. Wandering through the small stairways to the various plazas and fortresses is a many hour adventure.