The wristwatch may now be an anachronism. Need the time? Check your cellphone.

But there are still plenty of people who cling to the comfort of slender hands pointing to numbers spaced around a dial under which an astonishingly intricate mechanism beats as delicately as a hummingbird’s heart.

For them, particularly those who need repairs on the vintage Cadillacs of the trade, like a Rolex or a Patek Philippe, there is Dimitrie Vicovanu’s meticulously arranged booth in Manhattan’s diamond district.

Mr. Vicovanu, 73, a courtly Old World gentleman who came to his craft late in life, not only repairs watches, but also restores them. He makes sure the dial face, the crystal, the case and the interior wheels, springs, screws, axles, pinions and rubies are replaced by original parts or, if they can no longer be obtained, are made by hand, replated or soldered to look virtually identical to the originals while keeping accurate time. A fine watch can have 400 parts, and repairing the innards is exacting.

“The stem of a watch has 12 dimensions, and if you get one wrong it won’t fit,” Mr. Vicovanu said in a Romanian-flavored English.