The Braidmen could face either Cork Constitution or Division 3 side Queen's University in the last-four. The Cork Con v Queen's quarter-final tie was postponed due to an unplayable pitch.
Garryowen, who continued their fine cup record with a 16-6 quarter-final triumph over Blackrock, have been drawn away to Dolphin or Galwegians in the second semi-final.
The Dolphin v Galwegians game, which was due to take place at Musgrave Park on Saturday, was also called off due to the adverse weather conditions in the Cork area.
Cork Con, the inaugural winners back in 2006, and 2007 champions Garryowen are the only previous holders still in contention to lift the AIB Cup this season.
Galwegians are hoping to become the first Connacht side to annex the title, while two more wins would see Ballymena keep the trophy in Ulster. Ballynahinch's giant-killing run saw them crowned champions last April.
Meanwhile, AIB Junior Cup holders Tullamore will have home advantage when they host highly-rated Armagh in a mouth-watering semi-final next month.
Tullamore took a step closer to winning back-to-back titles with an impressive 22-15 quarter-final success over Sligo on Saturday, while Armagh, first-time semi-finalists and the current Kukri Qualifying League Section 1 leaders, accounted for Cill Dara on a 24-3 scoreline.
The second semi-final will see Cashel or Monivea at home to City of Derry. The Cashel v Monivea quarter-final tie was postponed on Saturday due to an unplayable pitch.
Qualifying for their first AIB Junior Cup semi-final, City of Derry put in another big performance at Judge's Road when they overwhelmed Boyne by 45-5.
The AIB Junior Cup trophy has resided in Leinster for the past three seasons, with Seapoint (2007), Navan (2008) and Tullamore (2009) keeping it in the east.
2009/10 AIB CUP SEMI-FINALS:
Ballymena v Cork Constitution or Queen's University
Dolphin or Galwegians v Garryowen
2009/10 AIB JUNIOR CUP SEMI-FINALS:
Tullamore v Armagh
Cashel or Monivea v City of Derry
* Ties to be played on Saturday, December 19