Here's links to monthly average temps for two popular W. Caribbean ports. They show March slightly warmer, and as the previous poster mentioned, leaving the states will also be slightly warmer. We cruise that time of year due to price and it breaks up the long NE winters. Might be a little cool first nite on deck, but it's gorgeous the rest of the trip.
Grand Cayman: http://www.weather.com/outlook/trave...omnav_business
Enter your port of departure at the above sites and it'll give you those averages also.