First up is fourth seed Venus against Davenport in a repeat of the 2000 final won in straight sets by the elder of the two Williams sisters.
Venus also beat fifth seed Davenport in the 2001 semi-finals en route to her second successive Wimbledon triumph.
That high-octane duel will be followed by a muscular confrontation between Serena, still smarting after her French Open semi-final loss, and eighth seed Capriati, the only one of the quartet not to have triumphed at Wimbledon.
Serena will have revenge on her mind having lost a three-set thriller to Capriati in the 2001 quarter-finals at the All England Club.
Belgian fans, meanwhile, will flock to court one where French Open champion Justine Henin-Hardenne and the woman she beat in the Roland Garros final, Kim Clijsters, should progress to the last four.
Second seed Clijsters faces Italy's Silvia Farina Elia while Henin takes on the last surviving Russian, 18-year-old Wimbledon debutante Svetlana Kuznetsova.
