In 1998 the Swiss watch brand Exaequo Genève went out of business, ending production of its Softwatch, a cult favorite inspired by the misshapen clocks in a Salvador Dalí painting.

Now Exaequo is back, with new ownership, and offering a new version of the watch that looks as if it is melting on your wrist — a design its website said reflected “the aesthetics of the Surrealist movement and the concept of fluid and unconventional time.”

The Swiss brand initially had closed after Dalí’s representatives sued it for putting the artist’s signature on the watch dial without permission, according to those familiar with the brand history. But since then its Softwatch, which sold for a couple hundred dollars when it was released in 1990, has become a collector’s item. (An engraved model that Paul McCartney gave to a sound engineer sold in 2019 for $4,480.)

“It’s super-wearable and really nice in terms of how it sits on the wrist,” said Andrea Casalegno, a watch brand consultant and horology influencer who, under the name I Am Casa, has compiled an online history of the Softwatch. “It’s historical, it’s got great design. It’s got it all, in my opinion.”

Chris Zocchi, working with investors that included the Italian watch company U-Boat, revived the brand last year. And, because of his extensive knowledge of the original watch and his passion-filled posts about it on social media, Mr. Casalegno, 26, was appointed as an ambassador for the new Exaequo.