Upvote:8
There is public transportation from FLL to MIA using the combination of Tri-Rail and the FLL-TriRail Shuttle. The FLL TriRail Station is the Dania Beach Station across I-95. The Shuttle is timed to meet the train and is not continuous. The MIA TriRail station is essentially at the airport.
Details here: http://www.tri-rail.com/airport-connections/
Uber/Lyft would be about $40 from FLL to MIA. There is also a van/limo service that offers a flat rate FLL-MIA of $35, I think, it's been 3 years since I've used it.
Depending on the time of your flight and how many hours you have, you can take Amtrak to the Miami Station, ~$40. From there, an Uber would be about $10.