You might consider a limo service. I think the rental costs may be higher. You obviously don't want to rent a car for the whole cruise time and pay for parking in Miami. So you are looking at two one way rentals (and I'm not sure if you can drop a rental off at the Port of Miami. SO, you are looking at the cruise line transfer costs, a taxi fare, or a limo service. Price all three and see which is the best option. There are other cruise chatters that have done this, so maybe someone with experience can shed some light. But don't make your transport overly complicated just to save $20 on it (rental pick up / drop off hassles etc..) The taxi or limo are probably you best bet unless there are a large number of you in your party.
Carnival Cruise Lines:
Fantasy 90, Celebration 95, Victory 05, Conquest 05, Spirit 6/06, Freedom 6/08, Holiday 7/08, Victory 6/09, Valor 9/09, Dream 6/10, Splendor 8/10,Conquest 8/11,Magic 11/11,Triumph 4/12,Spirit 7/12,Freedom 11/12, Triumph 2/13 - The fire cruise, Magic 1/14, Freedom x 2 6/14
NCL Dream October 2006, RCCL Mariner OTS June 2007, Celebrity Silhouette 2013