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:
Departing
T-1 220p, T-2 221p, T-3/4 222p
Departing
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.