Watches make up only a small fraction of sales for LVMH, the biggest luxury goods empire in the world. The group is far better known for Louis Vuitton leather handbags and Moët Champagne. But lately, with Swiss watch exports reaching record highs and growing interest in fancy timepieces from a new generation of wealthy global consumers, LVMH is showing heightened focus on its fine watchmaking business, which includes TAG Heuer, Hublot and Zenith.

Last week, Miami hosted LVMH Watch Week. On Tuesday, a glittering new prize was unveiled at the Fondation Louis Vuitton, the soaring glass museum designed by Frank Gehry to house the art collection of Bernard Arnault, the LVMH chief who is also the richest person in the world (this week anyway).

The bash on Tuesday night was a celebration to announce the winner of the first edition of the Louis Vuitton Watch Prize for Independent Creatives. Five finalists were vying for a 150,000-euro prize and a yearlong mentorship from the luxury house, rewards similar to those received by the winner of the LVMH Prize for Young Fashion Designers.

Nearly all of the 250 guests wore black; many carried Louis Vuitton handbags. The talk was all about the inner workings of eye-wateringly expensive timepieces, an impenetrable dialect for anyone who doesn’t speak “watch.” Mingling with watch-world titans like Rexhep Rexhepi and Carole Forestier-Kasapi, snippets of overheard conversation included: “My god! He is the Mozart of the mechanical movement!” and “Now there is someone who really understands their way around orbital complications.”

Jean Arnault, 25, the twinkly-eyed youngest son of Bernard Arnault and the director of watches for Louis Vuitton, was the evening’s host. The new prize is his baby (though he was not a member of the judging panel). His parents and his glamorous girlfriend, the influencer and YouTube strategist Zita d’Hauteville, watched proudly as he presented the award.

If his recent executive appointments are anything to go by, Bernard Arnault sees the world of watches as a place where some of his children can learn the ropes of running a luxury empire. Last month, Frédéric Arnault, 29, the former chief executive of TAG Heuer, got a new role: chief executive of the LVMH watch division. Another Arnault brother, Alexandre, 31, is the executive vice president for product and communications at Tiffany & Company, which has a sizable watch arm.

“We expected a hundred applications at most, and we got more than 1,000,” Jean Arnault said after the ceremony. He stressed that the goal wasn’t to get access to or hire young watchmakers for big players. “This prize was set up to make sure the power of Louis Vuitton can support independent talent,” he said. “The volume of interest we received shows that this is a world that can and wants to grow.”

All five finalists were well-known names in the industry. All were European men. Their creations, each out-glistening the other in an attempt to demonstrate a new and expensive way to tell the time, ranged from wristwatches to a desk clock controlled by a pocket watch and a bee-shaped automaton.

There were 20 semifinalists, some of whom came from France, Canada and the United States. “That even one semifinalist came from outside Switzerland was a big surprise to me,” Mr. Arnault said. “We also had one female semifinalist, which was very important and a big win for me personally, given that women are still not well represented in the watch industry. I hope even the presence of one is inspirational.”

The winner, Raúl Pagès from Neuchâtel, Switzerland, learned his trade as a watch restorer before becoming an independent watchmaker. Today the 40-year-old Mr. Pagès creates about four timepieces a year, crafting them entirely by hand, from the design and development of the mechanism to manufacturing, assembly and finishes.

His winning wrist watch design, the RP1, is a manual-winding stainless steel watch with a rare and nearly impossible to construct caliber fitted with pivoted detent escapement, a device in mechanical watches that transforms the energy from the unwinding of a coiled spring (the power source) into countable impulses. Mr. Pagès spent three years working on the watch before it was ready to be revealed. The price tag is close to $100,000.

Mr. Pagès said that he wanted to bring his vision for an RP2 to life, which would be a chronometer with “a totally new movement.” A chronometer is a highly accurate timepiece that meets stringent independent tests. He also wanted to expand his workshop to increase current production.

The prize will be awarded every two years. To make the competition more accessible, Mr. Arnault said he was considering expanding the number of awards to include concepts.

“I’d love to have people submit drawings and present dreams, although there are lots of legal implications that we have to consider,” he said. “ But we want independent watchmaking to grow in a healthy way. We have to figure this out next time round.”