Short answer - Yes.
You're just going to have to call. Age of boat, size, value will all affect it. I spoke to my broker just the other day about this and was told they won't cover me unless I already have sailed in the Caribbean (I have). Waiting to hear back on how much they will want. A friend of mine bought a boat in Trinidad. He could only get insurance from Loyds. I don't know how much it was but, it was not cheap.