The Cayman Islands requires proof of a negative Covid test taken within 24 hours of departure to enter. Ms. Yi and Mr. Tracey had booked P.C.R. tests through N.Y.U. Langone medical center one day ahead of their Dec. 24 departure. She received her negative test results on the evening of the 23rd. Mr. Tracey’s test also came back negative — after 34 hours, a missed flight, $150 in change fees, a two-hour wait for two rapid antigen tests and a back-and-forth trip to John F. Kennedy International Airport.

“It was definitely a memorable start to our trip,” said Ms. Yi.

Frequent testing, combined with vaccines and masking, have been repeatedly cited as the key to a holiday season closer to the “normal” of prepandemic times. But for international travelers who need tests to enter their destinations, getting tested in time is easier said than done. Finding a test has become increasingly difficult — appointments are booked and walk-in sites often have hourslong waits. And even if you can get a test, it is far from guaranteed that your results will come back in time for you to board.