There are so many variables to this question there is no right answer.
I boarded a ship in Boston and was so early that I walked right on and had to wait hours before my cabin was available. It was a small ship and the only one in port.
The Florida ports are massive and host many ships on any given day, but they are so adept at it that they make it seem effortless..in the interest of full disclosure, I've only sailed from Ft. Lauderdale, not Miami.
The weather can also be a factor, sometimes fog can delay ships getting in as well as flight delays.
The bottom line is what works best for you. If you're staying at a local hotel, I'd stay and relax until check-out and just plan on an hour to get into the terminal and board the ship. Often the vehicle traffic going in is the worst part. If you're taking a shuttle, have your camera ready, you'll have gorgeous panoramic views of many ships.
Remember that any carry-ons you bring will have to be carried around. You usually can't get to your cabin until 1:30 or 2, so bring what you need but travel light.
The fewer things you carry aboard, the easier the screening process. The lines tend to move fairly quickly and remember, every one is on vacation, unlike the airport, so the mood is more upbeat.
And finally, be smart. Have your documentation in order. Have your tickets available, have your passport out. And don't try to smuggle alcohol or other items on against policy. They will catch you and your vacation will start on a sour note.
In October we arrived at the Port of Miami at 11:30am and were on the Liberty by 12:30pm. In January we arrived at the same time and weren't allowed to board the Liberty until 2:30pm. It ususally has to do with customs and how fast they deal with the turnover of passengers and crew.
I recommend that you plan for the worst and remember that you are on vacation and soon will be sailing off with a smile on your face. Too often I see passengers get very upset while boarding and seems like such a waste of energy and terrible way to start a vacation.
Enjoy your cruise!
2002 Adventure, Explorer
2003 Navigator, Serenade
2004 Voyager, Adventure
2009 Liberty, Enchantment
2010 Independence, Liberty
2011 Liberty, Freedom
2012 Freedom, Freedom, Independence
Feb 2013 Liberty
Mar 2013 Liberty
Nov 2013 Independence
It depends on what kind of person you are and how you handle lines/waiting, etc. For example, if you arrive really early, like 10:30am...you will likely be one of the first people on the ship, however, you will have to sit and wait in the terminal for a long time. If you arrive later, say 1:30, you will like join a very long line that will trudge along very slowly, but there won't be much sitting and waiting...just standing and waiting!
This has been my experience. I personally like to arrive as early as possible at the port and get to the buffet on the ship early, because, after about 2:00 or so, it is jam packed. Of course, this all depends on many other factors beyond your control, so just go with the flow, and don't get upset.