Years ago, Nell Newman was rooting around for a pencil in the Connecticut home office of her late father, the actor Paul Newman, when she unearthed two horological treasures: a pair of Rolex Daytona watches worn by Newman in his latter years. 

"There they were with his driver’s license," said Ms. Newman. "They were just in a box on his desk." 

Now the pair of chronographs is destined to cause a commotion in the watch world when they’re put up for auction in June at Sotheby’s, part of the sale of more than 300 mementos from the estate of Newman and his wife, actress Joanne Woodward. 

Sotheby’s has estimated $500,000 to $1 million per watch, though watch experts say they’re likely to fetch more than a million dollars each. 

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One of the most coveted provenances in horology is having been strapped to Newman’s wrist. 

"We can tie vintage-watch collecting, vintage-Rolex collecting to him," said Andrew Shear, a watch dealer in New York City. "The Hustler" actor persistently wore Rolexes throughout his lifetime. He is most closely associated with the Daytona model; his late-1960s version with an "exotic" dial sold for nearly $18 million in 2017.

Mr. Shear speculated that simply because Newman used these watches to track his lap speed or ensure he wasn’t late for dinner, it adds hundreds of thousands of dollars to their value.

Were he still alive, the Hollywood icon may balk at such princely prices. "He did not put his watches on a pedestal," said Ms. Newman. For her father, watches were "all about keeping time, being on time and timing race cars." 

She recalled that he had the "quirky habit" of betting houseguests a quarter that his Rolex kept better time than whatever was on their wrist. He’d call a "What time is it?" hotline, hold up the phone to prove his watch was more accurate and collect his reward.

The first timepiece, a 1993 Rolex reference 16520 "Zenith" Daytona with a pearly white dial, was awarded to Newman in 1995 when his racing team won the 24 Hours of Daytona Race in Daytona Beach, Fla. At 70, Newman was the oldest person to win that race, and the watch is reverently inscribed: "Rolex at Daytona 24 Paul Newman Rolex Motorsports Man of the Year 1995". 

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The championship ticker has come up for auction before. In 1999, Newman donated it to the "Famous Faces" sale held by Antiquorum and Tourneau. Other marquee benefactors included Elton John, Madonna and Arnold Schwarzenegger. Newman’s steel watch hammered at $39,000, which he directed to his charity "The Hole in the Wall Gang," a camp for children with cancer and other life-threatening illnesses. (The actor, the founder of Newman’s Own, was also known for his philanthropic ventures.) 

While that is a relatively meager sum when stacked up against today’s celebrity-watch sales, Newman’s Rolex notched the highest sales price in the auction.

That ’93 Daytona meant so much to Newman that either he or someone in his life later repurchased the watch. So low-key was Newman about his watches that his daughter wasn’t previously aware of the buyback tale. "That was news to me," she said, "And I thought, what a delightful story."

The second Rolex is a later model—a 2006 white-gold reference 116519 Daytona on a black leather strap. The watch, at auction for the first time, is one of three known models given to the blue-eyed actor by Ms. Woodward, and bears the inscription "Drive Very Slowly Joanne" on the caseback. 

A variation of that gentle chide is inscribed on all the known Rolexes the actress gave to Newman—a reminder to the auto enthusiast to always keep his eyes on the track. 

Photos from 2008 show Newman wore the white-gold watch at Lime Rock Park in Connecticut during his final racing laps. He died that year.

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Recent hammer prices indicate that the watch world has Newman mania. In 2020, Phillips auction house sold a Rolex reference 6263 watch given to Newman by his wife, with the inscription "Drive slowly, Joanne," for nearly $5.5 million. The sale of Newman’s Rolex Daytona reference 6239 for $17.8 million three years prior remains the high-water mark for his watches. 

The actor received the watch from his wife around the late ’60s, coinciding with the start of his time-consuming side-gig behind the steering wheel. (Newman was said to have become a checkered-flag fiend after starring in 1969’s race-car drama "Winning" alongside Ms. Woodward.) As The Wall Street Journal has previously reported, Ms. Woodward likely purchased it for around $300 at Tiffany’s. On its caseback is—you guessed it—the inscription "Drive Carefully, Me." 

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Rolex introduced the model in 1963 and stopped production by the early ’70s, with about 14,000 made in total. Of that, only a couple thousand carried the idiosyncratic black, white and red exotic dial of Newman’s model. But photos of Newman brandishing this hard-to-find watch sent collectors on the hunt—sending prices to the ceiling. Eventually, watch aficionados dubbed this scarce style the "Paul Newman" Daytona. 

Today, even exotic-dial Daytonas that never touched Newman’s wrist sell for well into the six figures.