No, the Holiday Inn Port of Miami does not offer a shuttle to the port. (It's basically across the street fro the port, but it is still a mile and a half walk to the ships.)
They WILL get you a cab and the cost is about $15 (there is a port entrance charge the cabs will pass on to you).
They wil also store extra luggage down stairs for you in baggage claim. So if you are spending the night, pack an overnight/carry on for the night and store the rest in their baggage calim so you don't have to hassle bringing it up and down.
Carnival Cruise Lines:
Fantasy 90, Celebration 95, Victory 05, Conquest 05, Spirit 6/06, Freedom 6/08, Holiday 7/08, Victory 6/09, Valor 9/09, Dream 6/10, Splendor 8/10,Conquest 8/11,Magic 11/11,Triumph 4/12,Spirit 7/12,Freedom 11/12, Triumph 2/13 - The fire cruise
NCL Dream October 2006, RCCL Mariner OTS June 2007, Celebrity Silhouette 2013