The last four ballot, which took place at Mossfield Park in Oban on Monday, also saw Kingussie drawn to face Oban Camanachd or Kyles Athletic in the other tie.
And Bute will already be planning their revenge on the cup holders after a cruel defeat in last year's semi-final, when John MacDonald's goal in the 11th minute of injury time snatched a 2-1 victory for the An Aird outfit.
Bute qualified for the semi-finals with a stunning 7-4 win over Inveraray in Rothesay on Saturday (click
here for report), while Fort William required extra time, and a Brian Simpson hat-trick, to edge past Kinlochshiel by a 3-2 margin.
The semi-final ties are due to be played on August 15, with the final itself to take place at Mossfield Park on September 19.