The taxi fare is $24, plus $2 (I'm assuming for the toll that you have to pay to get to the port from Miami). I just got back from my cruise on the Majesty, and I can guarantee you that you're going to love it!
Also, just tell the cab driver that you want to go to The Port of Miami to the Majesty of the Seas. Royal Caribbean uses the Port of Miami.
2007 - Majesty of the Seas (Bahamas)
2009 - Enchantment of the Seas (Western Caribbean)
2010 - Freedom of the Seas (Western Caribbean)
2013 - Golden Princess (Alaska, roundtrip from Seattle)