Rain forced the postponement of the men's quarterfinals to Friday, when American Andy Roddick is scheduled to face Italian Fabio Fognini.
No. 4 seed Bartoli was tied with Safarova in the first set before she used a backhand winner to break for a 5-4 lead. She dominated the second set, giving up just two points on her serve before wrapping up the match with an ace.
"So far I'm able to play well and to stay consistent into my matches, which is really important on grass," Bartoli said.
Kerber was ahead 3-1 in the second set when play at Eastbourne was suspended because of rain. When it resumed 2 hours and 40 minutes later, Makarova held serve and then earned two break points. Kerber fought off the threat and went on to reach her seventh semifinal of the year.
"I was a little bit nervous, but I just tried to focus on me, tried to make my game plan and to play until the end," Kerber said. "I'm happy to manage this and go out there after the rain delay and win the match."