The draw at Murrayfield also produced a local derby in the other game as Boroughmuir will travel to Edinburgh Accies. The ties are scheduled to take place on Saturday 21 April.
West of Scotland coach John Beattie and Boroughmuir flanker Angus Martyn made the draw. West have secured promotion from Premier Division 3 and accounted for Kelso and Dundee HSFP on their cup run, and Beattie said: "It's a hugely interesting draw and very scary too.
"To play against Hawks is one of those mountains to climb because they have a hugely talented pool of players and they're fit but we're just going to go out and have a bit of fun."
The draw for the National Shield pits Garnock or Marr against Ardrossan Accies or Cumbernauld, and Musselburgh or the winner between Falkirk and Dalziel to play either Annan or Irvine. The catch up ties are to be played this Saturday.
National Cup semi-finals: Edinburgh Accies v Boroughmuir (21 April).
National Shield semi-finals: Garnock or Marr v Ardrossan Accies or Cumbernauld; Falkirk or Dalziel or Musselburgh v Annan or Irvine (catch-up ties due to be played this Saturday are: Garnock v Marr; Ardrossan Accies v Cumbernauld; Falkirk v Dalziel; and Annan v Irvine).
National Bowl semi-finals: Dumfries v Glenrothes or East Kilbride; Hillfoots or Waysiders Drumpellier v Kilmarnock or Morgan Academy FP
National Plate semi-finals: GHK v Ross Sutherland; Aberdeen University v Crieff or Strathearn.
(Finals Day on Saturday 5 May)