Federer is taking on 22nd-seeded Frenchman Adrian Mannarino before Williams faces Evgeniya Rodina in a matchup of the only two mothers remaining in the tournament.
After a series of upsets made this edition of Wimbledon the first since it began seeding players in the 1920s that none of the top 10 women reached the quarterfinals, Nos.
Williams looked to be in a spot of bother when she surprisingly lost the opening set 6-3 and struggled with consistency from the back of the court.
The 26-year-old faces German 13th seed Julia Goerges or Croatian world number 55 Donna Vekic on Tuesday. I just tried to fight for every point. "You can be a mom, you can still play tennis and you can still be great", Williams said afterwards.
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She steadied herself, though, and had a break point when Williams served at 4-2, but her chances were few and far between as her opponent continued to charge through a draw blown wide open by an exodus of seeds. As she keeps reminding folks, this is just her fourth tournament since missing more than a year of action because she was pregnant and gave birth to a daughter last September. Also still in the running is No. 12 seed, Jelena Ostapenko of Latvia.
"You never know what to expect from her [Ostapenko]", Cibulkova said.
On Wednesday, Federer will play No. 8 Kevin Anderson, a South African who was the 2017 U.S. Open runner-up and advanced with a 7-6 (4), 7-6 (2), 5-7, 7-6 (4) victory over Gael Monfils.
Williams, however, lifted her intensity in the second set, avoiding any break points as she secured one break of her own.
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Williams faces Camila Giorgi of Italy next, while 11th-seeded Angelique Kerber plays Daria Kasatkina of Russian Federation. But despite how close she is to another title and the record books, Williams is insistent that she doesn't need to win here in order to feel like her comeback has gotten off to a successful start.
Goerges had failed to make it past the fourth round of any major before this tournament, and her best Wimbledon finishes were third-round appearances in 2010 and 2011.
Rare is the player who can produce Williams' sort of pace on serves - Giorgi's average speeds were actually faster on first and second serves, and she delivered the match's first three aces - and mirror her power in groundstroke exchanges at the baseline.
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