Serena, who was ranked No.25 coming into the tournament after taking an extended leave to give birth, breezed past another mother on tour, Evgeniya Rodina, in two straight sets after the loss of just four games - 6-2 6-2, in just 64 minutes.
Federer dropped a mere five points in the opening set against Mannarino and saved his first break point with an ace.
Federer's progress through the draw has been smooth and serene, not dropping a set nor losing a service game on his way to an Open era record 53rd Grand Slam quarter-final.
Anderson, 32, is one of the biggest servers on tour and the hot conditions are helping his game, however, the 2017 US Open finalist has never taken a set off Federer in four previous meetings.
Federer took his tally of consecutive sets won on London's hallowed grass courts to 32 with a 6-0 7-5 6-4 dispatch of unsafe French left-hander Adrian Mannarino.
Novak Djokovic insists it's only fair that he should play his Wimbledon quarter-final on Centre Court on Wednesday, handing the All England Club a dilemma over relegating Roger Federer or Rafael Nadal to Court One.
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A look back at their last semi-final run
Ahead of their biggest game in a generation, Southgate has told his players the next few days can change their lives for ever. There was a surprise inclusion among the 23 players as a rubber chicken was thrown around in the early part of training.
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"Of course, it is important for me to be in these quarter-finals. I didn't play on grass for a whole year", Nadal said. Hopefully, it doesn't come full circle and my gloating come back to haunt me in the shape of Anderson playing lights out!
"It was crucial for him to stay in the match at the beginning of the second set and then it got tougher", said 20-time major victor Federer. Djokovic reached his 41st career major quarterfinal, tying Jimmy Connors for second all time.
It has been seven long years since the world No.1 has reached the final eight in London.
For all those punters convinced of a Roger Federer and Rafael Nadal final on Sunday, it is worth recalling a cautionary tale from a decade ago. As for his level I think he looked decent but not in spectacular form, Vesely was a real disappointment though, his forehand was powder puff stuff, loopy and it just sat up waiting for Rafa to take charge.
On Wednesday on Centre Court, he will start as underdog against Nadal, the 17-time major victor who is in the quarter-finals at Wimbledon for the first time since 2011 when he went on to finish runner-up. He's played there a few more times than that. "I feel like the more experienced you are, the more you can deal with those better".