Holders Rangers will visit Celtic in the SWPL Cup semi-finals, with Hibernian facing visitors Aberdeen in the other last-four tie.
The games will be played on or before Sunday, 19 January.
Rangers, who beat Partick Thistle 4-1 in last season’s final, had the biggest quarter-final win with Jo Potter’s side defeating hosts Motherwell 8-1.
Celtic and Glasgow City could not be separated after 120 goalless minutes and Elena Sadiku’s team triumphed 4-3 on penalties. They also host Rangers in Sunday’s SWPL encounter.
Grant Scott’s Hibs won 4-1 away to Thistle on Sunday and Aberdeen, with recently appointed boss Scott Booth in charge, also won on the road, 3-1 against Boroughmuir.