We just returned from a Royal Caribbean cruise. I hope this information is helpful to anyone leaving from the Port of Miami.
We flew in the day before and stayed at the LaQuinta Hotel on LeJeune Road. It was great-clean, delicious breakfast and helpful staff. It is near the airport, but we could not hear the planes taking off or landing. The hotel provides free shuttle service from the airport to the hotel and from the hotel to the Port of Miami. Nice $$$ saver. If you are using their shuttle service to the port, sign up for a time when you register. We took a taxi to Bayside in the evening, $20 one way.
After the cruise we got in a long line for a taxi ride to the airport. We were told that there is a standard rate of $25 per taxi (not per person) from the port to the airport. The line was long. While waiting in line, a man from a shuttle service asked if we wanted a ride to the airport for the same cost as the taxi ($25 for two people). There were four couples who took advantage of the ride. I don't know the name of the company, but the shuttle was clean and delivered us to our terminal. There were several families waiting for the Royal Caribbean shuttle to take them to the airport, I believe they charge $20 per person and you had to make reservations in advance, that's what someone in line told us.