There are shuttle companies that run between FLL and Miami. I don't think Super Shuttle runs out of FLL. Shuttles pay by the person and not by the van so with two or three people you may end up paying as much, or more than a taxi or limo. If you have three people plus luggage, a limo service may be the way to go.
You can Google a number of Limo services for the Fort Lauderdale and Miami areas. I have done this and the price was about equal to a taxi.
The bad part about flying into FLL is that while the airfare may be somewhat less expensive, the transportation can offset that cost.
I would also suggest posting this on a couple of the other boards, such as Carnival and Royal Caribbean to see some other responses.
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Probably the least expensive and easiest way to do what you want is to do a one way van rental at the airport (Dollar Rent a Car is obscenely inexpensive) and before you return the car at the airport drop off most of your passengers and your luggage at the port. Then one or two of you can return the van and take a cab/shuttle to the port to join the rest of your party. It's a piece of cake really. We did that once when we flew into Orlando and spent a few days there, then took a one way rental down to FLL. It was less than $20 a day with unlimited mileage, and ended up getting upgraded to a nice big roomy Durango, rather than a Jeep Cherokee.