Strange but true: Sharapova and Vandeweghe have never played. Each will come into their first meeting having not dropped a set in their first four matches at Wimbledon. You expect that from Sharapova, a five-time Slam champion, especially when she faces the middling competition she has faced so far. You certainly don’t expect that from Vandeweghe, who will be playing her first quarterfinal at a major. The American has been as cool and confident as any player in the tournament so far; will she be able to keep that cool when she’s upgraded to Centre Court? If she can, she has the weapons, particular on her serve and forehand, to win. But you have to think there’s a reason Sharapova is ranked fourth and Vandeweghe is ranked 47th. Winner: Sharapova

They played twice during the clay season, and the result was the same, a drama-filled three-set win for Serena. The first time, in Madrid, Azarenka snatched defeat from the jaws of victory by double-faulting with the match on her racquet; the second time, in Paris, Serena snatched victory from the jaws of defeat by coming back from a set-and-break deficit to play some excellent tennis.

Each came up with her best match of the tournament, and perhaps the best of the last two months, on Monday. Serena straight-setted her sister Venus, and Azarenka did the same to up-and-comer Belinda Bencic. Judging by her form, and how close she was to beating Serena the last two times, it’s tempting to say that Vika is due, and guess that fate will finally be on her side. But not tempting enough to make me do it. Winner: Williams

Muguruza won their only meeting, 6-0 in the third set, at the Australian Open this year. Both have made strides since then: The Spaniard is in her second straight Slam quarterfinal, and the Swiss is bidding to make her second straight Slam semi. Both pound their top-notch backhands and go for their shots, but Muguruza’s serve is a little better, and her forehand may be a little more reliable. Winner: Muguruza

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Wimbledon Women's Quarterfinal Previews

Wimbledon Women's Quarterfinal Previews

Radwanska is 3-0 vs. Keys, and she won their only meeting at Wimbledon. But those matches all took place at least two years ago, when Keys was a teenager; even then she took Aga to a third set at the All England Club. If nothing else, this match shows the versatility of grass: Keys likes it because of her raw power; Radwanska likes it because she doesn’t have much power, and it helps speed her shots up.

Keys could be a Wimbledon champions someday, and if she gets on a roll, she could mow Radwanska down. But for now, Aga is the former finalist, the perennial Top 10 player, and the woman who is in the middle of a long-awaited rebound. Winner: Radwanska