In 2022, several months after Joseph Barreto retired as a high school guidance counselor in East Harlem, he got a keepsake gift: a 42-millimeter stainless steel Omega Constellation watch with a grayish-taupe dial and prominent date display.

But getting the timepiece wasn’t as straightforward as, say, walking into Omega’s Fifth Avenue boutique. Instead, the Hackensack, N.J., resident traveled to Switzerland to buy it.

“Buying a watch in Europe is just a whole other experience,” said Mr. Barreto, 57. “They sit you down; there’s Champagne, there’s chocolate. It’s just an event.”

Many of the former students Mr. Barreto worked with over his 34-year career had given him money on his retirement, saying he should spend it on things to help commemorate the occasion. (“They’re family to me,” he said.)

His first purchase was a custom-made 14-karat gold pendant with diamonds and sapphires that he wears every day in memory of his father, who died in December 2019. “I had money, believe it or not, left over to buy the airline ticket for the trip,” Mr. Barreto said, “and still some left over to buy a watch.”

Mr. Barreto, who grew up in a blue-collar household, said his interest in watches was a personal thing. As he put it, “I’m a Puerto Rican from the Bronx — that’s not a Bronx thing, to get a watch that’s high-end.”