In case CCL-Carnival Cruise Line resumes operations on August 1 (as already announced), its ship's won't be visiting the Cayman Islands (a British overseas territory in the Caribbean). CCL’s website still lists a number of itineraries that include calls at George Town (Grand Cayman Island).
The country's Tourism Minister (Moses Kirkconnell) announced that the borders will remain closed until at least September 1, 2020. And that date might be pushed back further. The Caymans initially planned to reopen on June 1.
Last week, the country's Deputy Premier (Alden McLaughlin) said that the cabinet had passed a policy that Port George Town would not be open to cruise ships until September 1. He made clear that it was a tentative date as opposed to a guarantee, and the matter would be reviewed down the line. He added they were not consulted before cruise companies announced their George Town-visiting voyages.
Meanwhile, CCL is listing a number of voyages visiting Grand Cayman Island. For example, the August 2 & August 16 sailings of Carnival Horizon out of Miami include calls at George Town, Cozumel Mexico and Ocho Rios Jamaica. The August 24 itinerary of Carnival Sensation (5-night Miami roundtrip) visits George Town and Ocho Rios. The August 16 itinerary of Carnival Freedom (7-night roundtrip from Galveston TX) currently lists George Town, Cozumel and Montego Bay Jamaica.
For Coronavirus updates on cruise ship quarantines (infected passengers and crew) and top-pandemic countries (COVID-19 cases and deaths, daily updated statistics) see at CruiseMapper's Norovirus page.