Just 2 weeks ago, we arrived just after noon, and although we were inside in the air conditioning, it still took an hour and a half before actual boarding.
We met our friends onboard and they had been there well over an hour!
Oops, sorry, just realized that was Ft. Lauderdale, not Miami, but whatever the port, it all depends on circumstances of course.
Keep in mind that you will not be allowed in your cabin. Everyone will be herded to the Lido deck. If I remember correctly we were allowed in @ 2pm. You will be able to tour the ship and check things out. You will also have to drag along any carry on you would have with you. I suggest wearing your swimsuit.
Of course the food and umbrella drinks will be wonderful!!
Many cruise lines are not opening the cabins before 1:00 p.m. so I wouldn't rush to the ship unless you do not have a carry on, or it's a small one. This way you won't have to lug around a bag when you are touring the ship or sitting in the Lido buffet.
I used to be an 11:00 a.m. type of guy but now, if I can, I get there about 12:30 p.m. or 1:00 p.m.
On our last cruise that left from Brasil we arrived at 11:00 a.m. (because we had to be out of our hotel) and we're on the ship and in our cabin by 12 noon. The ship was almost empty for the next two hours when a huge flood of passengers boarded.
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When we were on the Carnival Freedom a few weeks back, they cleared the ship by 10am. As back-to-back cruisers, we had to meet in the atrium at 10:30am and were led ashore to be quickly processed. The crew was changing out at this time also. Once we re-boarded, they started letting new arrivals board, which was about 11am
1pm and later is quite crowded, because people tend to do as they are told. You can safely shoot for 11am
This appreared to be the schedule. As you well know, ship happens.