Weather has been an issue at the tournament in Belgium through the week. Play Friday was delayed but officials were able to get two quarterfinals, which were postponed by rain Thursday, completed.
As a result the semifinals and finals will be contested Saturday.
Hampton defeated second-seeded Roberta Vinci 5-7, 6-3, 7-5, winning just five more points (118-113) over the course of the 2-hour, 24-minute match. Hampton finished with seven breaks, including three in the final set.
Kanepi was a 6-3, 4-6, 7-6 (7-4) winner over seventh-seeded Varvara Lepchenko. Their match took 2 1/2 hours. Each player had six breaks but served better in the final set before Kanepi eked out the win.
Saturday's schedule calls for Kanepi and Hampton to meet in one semifinal while eighth-seeded Peng Shuai and Romina Oprandi, who won quarterfinal matches Thursday, meet in the other. The tournament final is to take place about 4 hours after the semifinals.