Roger Federer schools former USC star Steve Johnson at Wimbledon

As the grand old man of this tournament and a seven-time Wimbledon winner, Roger Federer has been around long enough to have played the guys behind the guys.

“It’s so funny,” said Federer, 34. “I’ve played some of the coaches.”

In the meantime, he’s happily taking younger players to school. The Swiss star, who hadn’t lost a set through the first three rounds, continued that trend Monday with a 6-2, 6-3, 7-5 win over former USC standout Steve Johnson. Federer advanced to his 14th Wimbledon quarterfinal, equaling Jimmy Connors’ Open era record, and tied Martina Navratilova’s record of 306 victories in majors.

On a day when two Americans, women’s No. 1 Serena Williams and men’s 28th seed Sam Querrey, secured spots in the quarterfinals — Querrey following up strong on his stunning upset Saturday of No. 1 Novak Djokovic — Federer’s familiar poise and precision were on display at Centre Court, where the crowd never stopped applauding him.

Those spectators know Federer is much closer to the end of his career than the beginning. He pulled out of the French Open in May because of a back injury, ending his record run of 17 years of consecutive Grand Slam appearances, an unbroken string of 65 majors.

“Clearly, I missed being in Paris,” he said. “But at the same time, for me it was really important to make the most of it, of those two, three weeks. Having a bit of a run here on the grass, now I’m happy it’s paying off.”

Next up for him is Croatia’s Marin Cilic — coached by onetime Federer opponent Goran Ivanisevic — who barely broke a sweat Monday in dispatching Japan’s Kei Nishikori, 6-1, 5-1. Nishikori pulled out during the second set because of a rib injury.

Federer’s most recent meeting with Cilic, in the 2014 U.S. Open semifinals, was momentous — the Croat won in straight sets and went on to beat Nishikori in the final for his only major title. Federer has 17 major titles, most among men, but hasn’t won one since 2012, at Wimbledon.

With Djokovic gone, Scotland’s Andy Murray, the 2013 champion, is the tournament favorite. But Federer isn’t far behind, making relatively light work of Johnson, who finished his USC career with 72 consecutive victories and a pair of NCAA singles titles.

Of course, winning a tournament means getting hot at the right time, and Querrey is scorching. He avoided a natural letdown after beating Djokovic and instead knocked off France’s Nicolas Mahut, 6-4, 7-6 (5), 6-4, to reach the first Grand Slam quarterfinal of his career, setting up a match against Canada’s Milos Raonic.

Querrey, a Thousand Oaks High graduate, said it was important for him, career-wise, to maintain his momentum after beating Djokovic, lest people look at that upset as “fluky.”

“I definitely knew if I lost, it would have been, ‘Hey, you beat Novak, but obviously that was just like one special moment,’” he said.

The Djokovic match was played over two days, with Querrey taking the first two sets before a rain suspension Friday, then finishing the job Saturday. Like a pitcher in the midst of a no-hitter, he didn’t talk tennis or even look at his phone Friday night. Since, however, he has made up for that.

“I’m not going to lie,” he said. “After the Novak match, I watched every highlight I could, over and over. Enjoyed the hell out of that moment.”

Querrey’s parents were in attendance for the Djokovic match, but they had to push their flights back to see the end of it. They flew home Saturday.

“My dad took the whole week off work last week, and my mom … I really don’t have an excuse for her,” he said with a smile.

Asked if his parents will come back to London if he makes it to the semifinals or beyond, he said: “I think they would, for sure. I don’t think they would hesitate to fly back for that.”

Four American women advanced to the round of 16, but only two emerged — sisters Serena and Venus Williams. CoCo Vandeweghe and Madison Keys were eliminated.

Serena Williams beat Russia’s Svetlana Kuznetsova, 7-5, 6-0, and moves on to face another Russian, Anastasia Pavlyuchenkova, who defeated the 27th-seeded Vandeweghe, 6-3, 6-3.

Venus Williams, whose five Wimbledon titles are just behind her younger sister’s six, beat Spain’s Carla Suarez Navarro, 7-6 (3), 6-4, and will face Kazakhstan’s Yaroslava Shvedova.

If both Williams sisters continue to win, they would meet in the final.

“I feel like she’s my best opponent, my toughest opponent,” Serena said of Venus.

Of course, neither is looking past her upcoming opponent. In Serena’s case, that means playing a woman she has faced five times — but never on a grass surface — going 5-0 and losing just one of 11 sets.

“I’ve lost to a player that’s never beaten me in the past in some big situations,” she said. “I definitely don’t want that to happen.”

Williams clearly is aware of what can happen, even to the world’s No. 1 player. (See: Djokovic, Novak.)

sam.farmer@latimes.com

Twitter: @LATimesfarmer