The Blues and Blacks haven't reached the Millennium Stadium for a domestic cup final since 1997, while Bridgend have to go back to 1990 for the last of their five appearances in the tournament's last round.
Bridgned beat Aberavon by a point, 20-19, in another game that went down to the wire, while Llandovery came from behind at Bedwas to beat their Premiership rivals 21-14.
"We are delighted to have come this far. It is the first time for the club to reach this stage," said 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 an historic occasion."
There was good news for Wales Sevens Coaches Dai Rees and Gareth Baber as some of their key players for the up coming Hong Kong and Adelaide Sevens came safely through the quarter-finals.
Cardiff full back Jamie Roberts got among the tries in his side's win, while Ponty outside half Dai Flanagan was in good form with the boot in his team's defeat at Llanelli. Scarlets flankers Rob McCusker and Jonathan Edwards will join Roberts and Flanagan on the plane bound for Hong Kong this week.
Konica Minolta Cup Semi-final Draw
Llandovery v Llanelli
Bridgend v Cardiff
Ties to be played the weekend of 14th April 2007
Kick Off times and Venues TBC - Matches to be played at neutral venues