Federer was followed by Serena Williams, she of the seven Wimbledon trophies among her 23 majors, who was hardly challenged in a 6-2, 6-2 win against 120th-ranked qualifier Evgeniya Rodina of Russian Federation.
With the top 10 women having all been eliminated, No 11 Angela Kerber is the highest-seeded player left in the tournament.
Ostapenko reached the last eight for the second straight year with a 7-6 (4), 6-0 victory over Aliaksandra Sasnovich, while Cibulkova beat Hsieh Su-Wei 6-4, 6-1.
Seventh seed Karolina Pliskova is the latest big gun to fall, the Czech crashing to a 6-3 7-6 (7-1) to big-hitting Dutchwoman Kiki Bertens. Serena needs to win three more matches to earn the 24th Grand Slam singles title of her career, a mark which would tie current record holder Margaret Court.
Williams and her sister were taught to play tennis by their father Richard, who devoted his life to training them on the public courts of Los Angeles. For me, I can't even think that far.
"This is only my fourth tournament back", Williams said.More news: Starbucks is eliminating plastic straws from all stores
The 2017 French Open champion lost her first two service games and was down 5-2 in the opening set before rallying to force a tiebreaker against her Belarussian opponent. "It's 115, and she puts the ball close to the line".
The 26-year-old faces German 13th seed Julia Goerges or Croatian world number 55 Donna Vekic on Tuesday.
'Each of us, seeded or not, I'm not seeded, we're just here to do our best.
Bertens, who was contemplating retirement past year after losing her enthusiasm for the sport, is the first Dutch woman to reach the Wimbledon quarter-finals since Michaella Krajicek in 2007.
In press conference after her third round Wimbledon loss to Su-Wei Hsieh, the world No. 1 Simona Halep admitted that she was exhausted mentally and physically after the French Open, which clearly influenced her performance at the All England Club.
Latvian 12th seed Ostapenko plays former Australian Open finalist Dominika Cibulkova.