Azarenka, the Australian Open champion, routed 14th-seeded Ana Ivanovic 6-1, 6-0. The match was briefly held up at 4-0 in the second set when Azarenka helped the ball boys pick up pigeon feathers that floated down onto the court from the roof. The Belarusian has dropped only 14 games in her four matches.
Radwanska beat Italian qualifier Camila Giorgi 6-2, 6-3 and will next play No. 17 Maria Kirilenko, who defeated Peng Shuai 6-1, 6-7 (6), 6-3.
Azarenka, Williams and Kvitova are the only women's players left who have reached a Grand Slam final — and they're all in the bottom half of the draw. Sharapova's defeat left four players in the top half who have yet to play for a major championship: Lisicki, Kerber, Radwanska and Kirilenko.
The first player to reach the quarters was 37th-ranked Austrian Tamira Paszek, who beat Italy's Roberta Vinci 6-2, 6-2 to reach the final eight for the second year in a row.
Leading Malisse 4-3 in the opening set, Federer left Centre Court with the trainer for treatment in the locker room. When play resumed eight minutes later, Federer didn't seem visibly affected — although the speed on his first serve lacked its usual velocity.
Still, in the final game, Federer hit two service winners and closed out the match with a 122 mph ace. He'll next play Mikhail Youzhny, who beat Denis Istomin of Uzbekistan in five sets.
The sixth-seeded Williams won the last three games to beat 65th-ranked wild card Yaroslava Shvedova of Kazakhstan 6-1, 2-6, 7-5. Williams hopped in joy with both feet in the air after hitting a big forehand that forced an error by Shvedova on the first match point, ending a hard-hitting contest that lasted nearly two hours.
Williams will next face Kvitova, who rallied from a set and a break down to beat former French Open champion Francesca Schiavone 4-6, 7-5, 6-1 in an error-filled match.
Williams has beaten Kvitova in their two previous matches, including in the 2010 Wimbledon semifinals.
"She's obviously a great grass-court player — as well as I am," Williams said. "I'll be ready."