The islands have managed to remain essentially virus-free partly because of their geography. Since most visitors arrive by boat, officials can monitor who arrives and check their health conditions and exposure history. They have taken measures including posting (official) notices at ferry docks, quarantining new arrivals, and conducting contact tracing of the few cases they do have.

On Fire Island, there have been no documented cases among its roughly 300 year-round residents, nor among the hundreds of summer homeowners, largely from New York City, who have flocked there in recent weeks despite the apprehension of the full-timers.

“A lot of people called and said, ‘We’re trying to escape the virus and need to get out of the city — can you open my house?’” said Gary Cuomo, whose property management company on Fire Island opens and maintains homes for summer residents.

Mr. Cuomo — no relation to Gov. Andrew M. Cuomo — has opened more than 100 of them in recent weeks, though he knows some of the year-round neighbors might not be happy about it. “Obviously, they’d prefer them to stay in Manhattan and not come out here,” he said.

Fishers Island, an exclusive sanctuary in the Long Island Sound just off the Connecticut coast, has set strong recommendations against migration onto and off the island and requires two-week quarantines both for newcomers and anyone who ventures off, even for a brief errand.