The port is directly across US1 from the airport. A cab is $10, I've never used a limo. I doubt they charge by the mile with a limo because you could literally walk there. I would assume most limo services are a flat fee. Have you tried googling Ft. Lauderdale limos?
For some reason that I don't recall, we used a limo for a cruise at Port Everglades a few years ago. For a Lincoln Town Car from FLL to the port it is now around $35 not including a tip - or you can get the same sized car (taxi) for maybe $15 including tip.
Of course we stayed overnight and therefore had three short limo trips in total for around $100. In retrospect it wasn't a good use of money.
