Yes, there are taxis available at the Port of Miami. $24 flat rate (plus tip) to the airport (MIA).
Here is a link:
http://www.miamidade.gov/portmiami/p...sportation.asp
Wait times and availability will vary for number of reasons (Number of boats in Port, when you disembark the ship, number of people using taxis, events in the City, etc.). In my experience, there have always been taxis lined up waiting for pax off the ships....