In SXM, when off a ship, because we would be snorkeling and because of our comfort level in SXM, I normally do not take my phone (unless had specific plans to meet someone) or have with me any of the phone numbers for the port agent or the cruise line - I would have color photocopies of our passports. Pretty much same on other Caribbean islands. If we were in a European port, I normally would take off ship my phone and a paper with some emergency numbers - I also might bring actual passports depending on country.