Which form of public transport will you be using. Also are you talking about going from airport to airport or someplace in the two cities?
Airport to airport.
And whatever form of public transit is quick, economical, reliable, and safe. I know there is train service in south Florida (Tri-rail ?) but I think you have to make a bus connection at both ends to use that.
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Arriving into FLL at 2pm, there is a Tri-rail train departing the FLL station at 254pm, arriving the MIA airport station at 337pm.
If your flight is late, the next train departs and arrives exactly one hour later.
The bus from FLL to the station will run as follows:
T-1 220p, T-2 221p, T-3/4 222p
T-1 323p, T-2 324p, T-3/4 325p
The bus from the station to MIA meets the train on arrival and takes about 3 minutes to get to the station.
The one-way fare is $3
If you did this on a Saturday, the only option is the 345pm train, which arrives at 437pm - still plenty of time.
If you were really late and missed both trains, you would need to take Tri-County Airport Express (http://www.floridalimo.com), and their fare is $40 one way for 2 people plus a luggage charge. If you want to skip the train altogether and pay the $40, you can call ahead to reserve seats on the shared van and just do that instead.
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Tri-Rail is not really a "traditional" public transit system, but is really a work-commute-oriented system that (by design or happenstance) runs near the three area airports.
One thing you might do to help save time on arrival is to have an understanding of where the bus stops are at FLL (the signage is not the best). You may wish to contact the FLL airport authority and Tri-Rail to get instructions as the the exact location of the bus stop for the specific terminal that you will be arriving at: