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."
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