The crowd roared. People sprang from their seats in an explosion of cheers and applause. Serena Williams had taken the lead against No. 2 seed Anett Kontaveit during their second-round match at this year’s U.S. Open tournament.

It was yet another feat of tennis from a legend who transcends the sport, and fans could not get enough. When cameras cut to her box at Arthur Ashe Stadium, supporters including her husband, Alexis Ohanian; Tiger Woods; Anna Wintour, the Vogue editor; and others were seen on their feet, applauding. In the midst of the uproar, one supporter appeared calm, cool and collected: the tennis star’s mother, Oracene Price.

Her poised, enigmatic stare has become something of a trademark. Ms. Price, 70, has been a courtside fixture throughout her daughters’ careers. On Twitter, she is a fan favorite. (A clip of her talking to her granddaughter, Alexis Olympia Ohanian Jr., garnered nearly 50,000 likes.)

Over the years, supporters have noticed Ms. Price’s facial expressions during matches — she often wears sunglasses and rests her head on her hand, sometimes seeming to doze off.

Since Venus and Serena Williams turned professional in the mid-90s, Ms. Price has watched them play countless matches, including hundreds of Grand Slam matches. This U.S. Open, however, is unlike any of the tournaments Ms. Price has attended over the decades. Since Williams announced that she was “evolving away from tennis” in a first person essay for Vogue last month, her matches have been energized with a lightning-strike sense of magic and a palpable edge. The crowd — thousands in the stadium and millions at home, at watch parties and at bars — seems to hold its breath, wondering silently or aloud: Can she go all the way? Having won 23 Grand Slam singles titles, will this be her 24th, tying Margaret Court for the record, or will this be her last match?

There is a sense that, with Williams, we are witnessing history in the making. And in her second-round victory, her message was clear: She’s not done yet.

So, what would it be like to watch your children make history? To know that you raised two of the greatest tennis players of all time? As a mother of legends who has devoted most of her adult life to supporting their journeys as tennis stars, how can Ms. Price remain such a beacon of grace under pressure as she watches her daughter play what might be the last match of her career?

Anyone who has attended a youth sports game can tell you that many of the games are teeming with anxious, overbearing, competitive parents. It’s common to watch parents cheer, shout and occasionally explode with anger or excitement. Not Ms. Price.

Some online hypothesize that she is ready for her daughters to retire, or that, after all the touring, all the success over the years, she’s had enough of this part of her life. But that’s far from the case, according to Rick Macci, the Williams sisters’ former coach.

Mr. Macci coached the sisters for four years, in the early ’90s. He worked closely with both their father, Richard Williams, and Ms. Price to create the foundation for the girls’ careers. Mr. Williams “always had his foot on the gas,” Mr. Macci said, while Ms. Price had to be “the calming force.”

“You just become that,” he continued. “But obviously, she feels the pain and she feels the joy all through their careers every time they make a shot or miss it.”

But above all, Mr. Macci said, Ms. Price is a fantastic mother. “I think her personality — she’s very, very calm, very low-key,” he said. “She was amazing with the girls. She wanted to make sure they were kids. She wanted to make sure that they had a teenage life and she did everything possible to make that just as important.”

Mr. Macci said Ms. Price was “the master puppeteer” and the “backbone” behind the greatness of her daughters. “She was probably the best tennis mom ever,” he said. “Because she let Richard do the heavy lifting, and she was Mom. And that balance, all we can say is: How can you argue with the results?”

He added, “She should be in the Hall of Fame as a mom.”

Samantha Stevenson, a former freelance journalist who has written for The New York Times, and the mother of Alexandra Stevenson, a former professional tennis player, echoed Mr. Macci’s sentiment. Ms. Stevenson spent years touring alongside Ms. Price, as their daughters became fast friends when they were children.

When Ms. Stevenson first met Ms. Price, she was a reporter on assignment. She brought her daughter along to interview Mr. Williams and Ms. Price about Venus. Later, when Ms. Stevenson became a parent to a tennis star herself, she said she always looked at things from the perspective of a sportswriter and a mother.

“Oracene was looking for peace and grace,” Ms. Stevenson said. “And that’s how she carried in her life. So what you see in the stands is how she was everywhere.”

She continued, saying that Ms. Price deserves accolades and the title of “Best Mom.” “When you see her on the court and she looks like she’s sleeping, she’s not,” Ms. Stevenson said. “She’s just in her head, thinking. She’s seen a million points. What’s one more point that she misses? She knows Serena’s going to take care of it.”

And when Serena turns to this new chapter in her life, working on growing her family and her business, and evolving beyond tennis?

“Oracene will live the life with her girls and evolve with them,” Ms. Stevenson said. “Because that’s who she is: She’s their mom.”

What Ms. Price is truly thinking or feeling at her daughters’ matches will most likely remain a mystery to onlookers, but a 2019 interview with “Today” offers a clue. Ms. Price was asked what goes through her mind on the sidelines.

“Well, I’m watching their techniques, mostly,” she said. “But before they get on the court I’m watching their mental,” motioning to her temple. Later in the interview, Ms. Price added that she has learned to “just look at it for what it is. It’s a game. Someone’s gonna win, someone’s gonna lose.”