I was told that approaching and entering the mouth of the bay at Montenegro is incredible. I friend of mine did so when they chartered a sailboat for a week. Does anyone have experience hiring a boat for a day trip or taking a boat tour from Dubrovnik to Montenegro? I was told by a Croatian that relations between the countries is not great so that it is difficult to get a captain to go from Dubrovnik to Montenegro.

We'd like to do the same thing. Did you have any luck finding a boat?

I don't think there are any boat trips from Dubrovnik to Montenegro. These firms offer boat trips in Montenegro:
www.montenegrocruising.com
www.montenegrotourboats.com

Thank you for the reply.
The reason for the boat trip is that we will only have two full days in Dubrovnik after a long transatlantic flight and another long drive to Dubrovnik via Mostar from Hungary. We'd very much like to see Kotor Bay but I'm not sure we can take another day traveling in a car. The boat trip would make it interesting. Unfortunately it looks like we will have to give it up.

There is no need to drive from Dubrovnik to Kotor. Travel agents offer coach tours and there are regular buses:
www.libertasdubrovnik.com/voznired.swf