Cardiff will face local rivals Bridgend and Llandovery will meet Llanelli in the semi-finals of the Konica Minolta Cup (neutral grounds, 13-15 April). The Blue and Blacks advanced with a comprehensive 39-8 win over Swansea at St Helen's on Sunday, while Llanelli beat Pontypridd 37-30 at Stradey Park.
On Saturday, Bridgend claimed a thrilling 20-19 win at Aberavon.
Llandovery spoilt Bedwas' first quarter-final appearance by claiming a 21-14 away victory.
"We are delighted to have come this far, it is the first time for the club to reach this stage," said Llandovery director of rugby Iestyn Thomas.
"It's great to have such a prestigious regional derby against Llanelli.
"We've beaten them once in the league this season, and knocked them out of the cup last season, but the stakes will be higher this time.
"We're happy to be tagged as the underdogs and can't wait for what will be a historic occasion."