The ships can't dock in Grand Cayman, so you will transfer from the ship (while anchored) on to smaller boats that will take you ashore. You need to allow time for this, they let people with excursions booked through the cruiseline off first.
If you are not in a hurry to get off, you won't have to get a tender ticket or wait in line. Just have a leisurely breakfast and head down to get the tender when there's no line left (usually only 30 to 45 minutes after the tenders start running).
This may sound silly, but I enjoyed the tender ride. It was cool to look back and see our ship and all of the other ships just hanging out there. It was also cool to look ahead at the island coming up.
Honeymooned on the Star Princess Nov 2004
1st Anniversary on the Carribean Princess Oct 2005