Seven-time Wimbledon champion Federer reached his 13th quarterfinal at the tournament with a 6-2, 6-2, 6-3 win over Spain's Roberto Bautista Agut.
The 33-year-old needed just 96 minutes to clinch victory and goes on to face French 12th seed Gilles Simon for a place in the semifinals.
Federer holds a 5-2 career lead over Simon who reached his maiden Wimbledon quarterfinal by knocking out 2010 runner-up and sixth seed Tomas Berdych.
The Basel native star claimed victory on a sixth match point against Agut, whose challenge was seriously compromised by needing treatment on his right ankle after a bad fall in the sixth game of the second set.
Wawrinka struggled at times in his win over Belgian 16th seed David Goffin 7-6 (7/3), 7-6 (9/7), 6-4 to make the quarterfinals for a second straight year.
Wawrinka, seeded fourth, will face French 21st seed Richard Gasquet for a place in the semifinals.
The French Open champion is aiming to become the fifth man to win Roland Garros and Wimbledon in the same year.
In women's action, Swiss Timea Bacsinszky qualified for the Wimbledon quarterfinals for the first time after defeating Romanian Monica Niculescu in three sets.
She bounced back from a first set trouncing to prevail 1-6, 7-5, 6-2.
Swiss teenager Belinda Bencic, meanwhile, lost 6-2, 6-3 to Victoria Azarenka setting up a Wimbledon quarterfinal clash with Azarenka's old rival Serena Williams.
Top seed Williams earlier defeated sister Venus 6-4, 6-3 in her last-16 encounter.