Five-time champion Venus Williams reached the Wimbledon semi-finals for the first time since 2009 with victory over Kazakhstan’s Yaroslava Shvedova.
Eighth seed Williams – at 36 the oldest Grand Slam semi-finalist for 22 years – beat unseeded Shvedova 7-6 (7-5) 6-3.
An all-Williams final remains possible after top seed Serena beat Russian Anastasia Pavlyuchenkova 6-4 6-4.
In Thursday’s semis, Serena will play Russia’s Elena Vesnina and Venus will take on Germany’s Angelique Kerber.
“We don’t really talk too much about it but we are playing doubles later, so we are just happy to be in the semi-finals,” Serena told BBC Sport.
Asked about a potential final meeting, she added: “It will be great. Venus is such a tough opponent I want her to win so bad – not in the final if I am there, but if I’m not, I do.”
Kerber, the fourth seed, beat Romanian fifth seed Simona Halep 7-5 7-6 (7-2) in the opening match on Centre Court.
Unseeded Russian Vesnina thrashed Slovakian 19th seed Cibulkova 6-2 6-2 in the remaining quarter-final on court one.
‘I love playing the game’
Venus Williams showed she remains a real threat on the All England Club grass with an impressive win over world number 96 Shvedova.
The champion in 2000, 2001, 2005, 2007 and 2008 made it through to her first Grand Slam semi-final since the 2010 US Open.
At 36, she is the oldest major semi-finalist since Martina Navratilova finished runner-up at Wimbledon in 1994.
“I love playing the game,” Williams told BBC Sport. “When you’re winning matches it makes it that much sweeter.”
The American, who played her first Wimbledon in 1997, recovered from losing an early break to win the opening set tie-break from 5-2 down.
She then dominated the second set, racing into a 5-1 lead and holding off signs of a Shvedova comeback to serve out the win.
“What a tough day on the court,” Williams added. “The tie-breaker, it felt like she would win. I felt like my opponent was on fire.
“I felt like the crowd enjoyed all the great points. She got them involved in the last game. We gave them good tennis today.”