I don't believe any of the cruise lines offer transfers to Port Everglades from SFB.
A car service is going to be very costly since it's almost a 4 hour drive (250 miles), if yyou can even find one to make the run.
A car rental will probably be your best bet, but be forewarned... traffic is horrendous when you get that far south and the toll roads are Cashless (Sunpass Only)
The other option would be to look at flying into FLL, may be more expensive than SFB but you will save on the ground transportation costs to the Port and the aggravation of driving in the area. There are very cheap shuttles to the port from FLL
Last option I would look at is, if you are firm on flying into SFB, you may be able to get a reasonably priced flight from SFB to FLL and co-ordinate your transportation this way.
I believe that you could use the train or the Megabus, but this would also involve complicated transfers to and from the bus or train terminals. Not worth your precious vacation time IMHO.
*****Another thought I'm going to throw out to you, if you're going to fly into SFB, why not check out the cruising options from Port Canaveral. It's much closer and ground transportation will be considerably cheaper.