The one time I flew into and out of PBI (West Palm Beach) we did a one way car rental between there and Port Everglades. This worked well because of the close proximity of car rental locations to the port.
With the Port of Miami this is a bit of a different story. Almost all rental company locations are at Miami International Airport (MIA). It is a $20 cab ride between the airport and the Port of Miami.
You can look into Enterprise rental car and see if there is a closer drop off point to the port of Miami.
There may also be limo or shuttle services but I do not know of any off the top of my head.