My wife and I just returned from a 7 day cruise aboard the Carnival Liberty out of Miami. We flew into Fort Lauderdale on Sat. May 31st and used Go Airport Shuttle (
www.floridalimo.com) to the port. The cost was $18/person plus tip and took about 30-40 minutes. Their pickup point is just outside the baggage claim area, lower level, curbside, contact one of their customer servies reps wearing a white shirt. We only waited about 10 minutes. There were six of us in the van and it was much quicker (and lesss expensive) than waiting for the Carnival transfer.
Things went very smoothly and from all accounts much less expensive than using a cab.
However we did use the Carnival transfer back from the port to the airport. This way we were one of the first off the ship and they had the responsiblity to get us to the airport on time for the return flight.
Enjoy you cruise.