I agree with peachfront. If you are in the Caribbean and going to the beach, diving, snorkeling, etc. your passport is much safer in the safe in the room.

When not cruising (land trips) I usually keep the passport safe - if staying in a private house, leave it there buried somewhere, if in a hotel, usually in a safe.

Often I carry a copy of the passport with me but since I have the passport number, issuance and expiration date memorized, I can give that info to a US consulate from memory.

John