On CP Western Caribbean, we had tender for Princess Cays & Grand Cayman.
For Monetgo Bay, we docked starboard side.
For Cozumel, we docked port side (could have very well had been starboard).
At Cozumel, there are 2 piers cruise ships can dock - one's further away from the main shopping mall while the other is directly across the street from it. We got lucky and were allocated the closer pier. The pier can accomadate 2 ships and it did for the two days - Carnival had the Sensation & Paradise docked starboard side, across the pier from us.