In March, she lost in the first round of the Miami Open to Naomi Osaka, leading to a hasty exit in which she bypassed a postmatch media session.
Williams is looking for her eighth Wimbledon title and has established herself as the big favorite once again, with the top-10 seeds all eliminated.
Williams, who has a kind run through to the semi-finals, will next take on Camila Giorgi of Italy.
The American superstar advanced as no top-10 women's seeds made the quarter-finals in 50 years of professional tennis following the fourth-round elimination of world number seven Karolina Pliskova. The reprieve was only momentary for Hsieh, as Cibulkova regained her composure to break and take the first set 6-4.
Williams, a 23-time major victor, is hoping to join a select group of women who have won Grand Slams after becoming mothers.
Through her four Wimbledon matches last week, Williams carefully had calibrated the speed of her serves, taking care not to aggravate the injured pectoral muscle that had forced her withdrawal midway through the French Open last month.
"I think she said, "I'm sorry", Bertens said. "I think it's a great week". And I feel like I'm back. "But when I come here, I come here thinking that I can do a good result, no?" "These are the matches we work so hard for, me and my whole team". "I went for it", Serena said.
Williams, 36, now heads to the semi-finals to compete against German tennis player, Julia Gorges.
Serena fought back from a set down to defeat the daring Giorgi, 3-6, 6-3, 6-4.
Angelique Kerber, the highest remaining seeded player in the women's draw at No. 11, finally converted on her seventh match point to advance to the Wimbledon semifinals.
Rebounding from her shock first-round elimination in her Roland Garros title defence, Ostapenko has marched through the Wimbledon draw without dropping a set.
Williams was forced to withdraw from the fourth round of the French Open last month in her grand slam return with a pectoral injury and admitted last week she still wasn't serving at full power. 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.
Next up for Kerber is Russian 14th seed Daria Kasatkina, who took out Belgian Alison Van Uytvanck 6-7 (6-8) 6-3 6-2. In February 2017, the star accidentally announced that she was expecting her first child via Snapchat.