My wife and I sailed out of Miami on the Liberty last month. We have the option of flying out of Newark, NJ (to Miami or Fort Lauderdale) or Newburgh, NY. We flew from Newburgh to FLL because of the flight schedule and it was more convenient, even thou the cost was about the same. We used Go Transportation from FLL airport to the port of Miami. Our plane arrived around 10:30, we grabbed our bags and the Go Transportation booth was just outside the baggage claim area at curbside. We only waited about 10 minutes to be pickup and the ride was about 30-45 minute ($18. pp plus tip). Everything went very smooth.
On our return we decide to take the transfer offered by Carnival ($24. pp) back to the airport. We were one of the first people off th ship and had plenty of time to check our bags and go through security (our flight was at 12:05). We found FLL airport less of a hassle and much easier to go through than Miami.
Hope this helps.