Is roaming free in Anguilla with my US, UK, or EU SIM card?

No! This is the #1 roaming trap. Although it is a British Overseas Territory, Anguilla is NOT part of the UK and NOT in the European Union. Your "Roam Like at Home" (EU) and standard UK carrier plans DO NOT APPLY. Most home carriers (like AT&T, Verizon, T-Mobile, or UK's Vodafone/O2) will charge you extremely high international "Rest of World" roaming rates (e.g., $10-$15 per day). A Cellesim eSIM is significantly cheaper.