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.