Kasatkina was more competitive in the second set but Kerber broke to go 6-5 up, then served out the match. Kerber found herself on match point six times before she finally broke through.
"She played well, especially when she was down".
Although Kerber eventually won 6-3, 7-5, it was a gutty performance from Kasatkina, who exited in the quarterfinal round for the second straight major. She lost her very first service game through two double faults, one on break point, which meant Kerber was 3-0 up after just 10 minutes. Kerber, though, hit most of what she could reach right back hard and flat, and only made half as many unforced errors.
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The 36-year-old Williams was absent from the All England Club in 2017 due to her pregnancy, and played her first Grand Slam since giving birth at the French Open last month when she reached fourth round. The 2017 French Open victor had 33 winners against just six for Cibulkova, and finished with five break points.
In the women's quarter-final on No1 Court, Ostapenko defeated Dominika Cibulkova in another match dominated by breaks of serve.
Ostapenko was more efficient, serving her match out at love and converting her first match point with her 14th backhand victor. The No 12 seed faces Kerber on Thursday.