Both semi-final ties will be played on the weekend of 14-15 November. Specific dates for the two semi-finals have yet to be arranged with broadcasters.
The Hughenden match is a repeat of last year's Celtic League quarter-final when Glasgow lost out 20-17 to Ulster. The teams have met already this season when Glasgow crashed to a disappointing 33-6 defeat at Ravenhill in Belfast.
Glasgow have shown great character and resilience to reach this stage of the Celtic Cup. A similar attitude and a big Hughenden crowd would give Glasgow a great opportunity to reach a major cup-final.