I have used the Carnival transfers from Orlando airport and it worked out just fine. You may find a shuttle service that works as well, totally up to you...It is a good 45 minute drive to the port from the airport, so a taxi would be way expensive...
All I ask is a tall ship and a star to steer her by; John Masefield
Carnival: Glory 2004, Destiny 2008, Splendor 2009, Freedom 2011, Valor 2012, Dream 2013
Celebrity: Summit 2011
Princess: Ruby 2010, 2014, Caribbean 2013, Coral 2014, Regal 2014, 2016
Star Clippers: Royal Clipper 2015