Ships time is always home port time. So Miami would be eastern time. Cozumel is actually on central time. But you would use the eastern time zone like the ship. Just set your watch to the ships time and you'll be fine
Not always true. On many voyages the clocks are moved ahead or back when crossing time zones.
SS Norway (12 times) '85 - '97; Radiance OS 06/01; Island Princess 11/04, Grand Princess 11/04/05, Golden Princess 7/21/06, Golden Princess 2/24/07, Explorer of the Seas 12/23/07, Island Princess 11/15/08
When I went Miami to Cozumel on Carnival in March, The ship time changed so much my head was spinning. And it did not match home port time during the cruise. There is plenty of warning-via announcements and the ships daily paper of the time to follow. When in doubt ask any Carnival employee. Remember the ship LEAVES on ship TIME! We left a couple of cruisers behind because they weren't paying attention.
On many voyages the clocks are moved ahead or back when crossing time zones.
I found this true on every one of the 10 cruises I've taken. I've never been on a ship that didn't change to island time.
Voyager of the Seas 5/03
Celebrity Solstice 2/09
Oasis of the Seas 10/16/10
My first few cruises we changed clocks like socks.. every day it seemed. The last few trips we stayed on ship time. Just dont ask people in port what time it is or look at a port clock. It could mess up your trip badly..
2008-Valor and Glory
2009-Spirit and Splendor
2010-Freedom of the Seas and Mariner of the Seas
2012-Allure of the Seas and Navigator of the Seas