Anguilla requires you to be vaccinated and provide proof of vaccination BEFORE you depart to Anguilla. They have a website - https://ivisit.gov.ai/ - that you need to complete, upload documents including a negative RT-PCR test that had to be taken 3-5 days before arrival. They will issue you an "Entry Certificate" that you need to show to the carrier brining you to Anguilla (either plane or ferry boat).

We came by ferry from Sint Maarten and were immediately tested (RT-PCR) again by Anguilla, and they snapped a yellow wristband on our arms. We could depart to the hotel and could not leave the hotel grounds until we received our negative test result the following day. We were tested at 2:00 pm, and our results arrived by 10:00 am the next day (by email). At that point, we could remove the yellow wristband and travel freely around the island.