It's 11:59 A.M. on a recent Wednesday and Clare Vincent, a 78-year-old associate curator at New York's Metropolitan Museum of Art, is perched before an ornate 17th-century clock on the Met's first floor, keeping a close watch on a technician winding the timekeeper.

Visitors wandering among the Met's paintings, mummies and other treasures probably don't notice that every European clock on exhibit not only still ticks but also tells the right time.

That's because for 40 years, Ms. Vincent, who oversees the museum's European timepieces, has been making sure they are wound like clockwork. Until recently, she wound up to 15 clocks a week on her own, climbing stepladders to reach into the tallest ones.