The draw has also been made for the last eight of the Irish National Cup.
Lurgan, the NCU's sole representative, are home to The Hills. Between them the sides have won the Irish Senior Cup five times so it gives both the chance to recapture past glories.
Glendermott, celebrating their 100th year will be praying for no rain on Sunday 14th June, as they host County Kerry, last season's beaten finalists.
Outsiders Sandyford will be looking to continue their cup run as they face Ballyspallen, while 2019 runners-up Ardmore entertain University of Galway, who knocked out holders County Galway in the last round.
NATIONAL CUP QUARTER-FINALS
- Lurgan v The Hills
- Glendermott v Co. Kerry
- Sandyford v Ballyspallen
- Ardmore v University of Galway
Ties will be played on Sunday June 14th
