To be played at neutral venues, venues tbc, weekend of April 17
The vastly experienced Davies, who has experienced top flight rugby with the likes of Cardiff Blues and Leeds Tykes during a distinguished career, has reached the cup final just once before but failed to come away with a winner's medal.
"I've played in a final before with Neath some years back against Newport," he recalled. "Unfortunately we lost that day so if we can get over the Pontypridd hurdle in the semis - which is not going to be easy at all - it would be lovely to go back and erase some ghosts of the past."
Quins' key play maker added: "It's an interesting draw against Pontypridd. We've played them once this season and beat them at home but it's going to be a lot different away from Carmarthen Park. We're looking forward to it but not overawed with the challenge Ponty are going to give us."
Pontypridd club secretary Steve Reardon is taking nothing for granted and expecting a tough battle against the Quins.
"They have already beaten us this season so it will certainly be a tough game for us but we are confident we can be competitive against any team at any venue so we'll give it our best shot."
Cardiff and Llanelli will face each other in the other semi final, just a week after taking on each other in the Principality Premiership.
"It's going to be a tough game but in terms of excitement of a cup draw against Llanelli, the cup kings, we can really look forward to it and plan for it," said team manager Gafyn Cooper.
"We have a game against them on April 10 in the Premiership and a week later we play them again in the cup semis so we are going to know a lot about each over the coming weeks. But we are looking forward to it immensely."
Cooper admitted his side's current SWALEC Cup campaign has captured the imagination of the club, particularly as they are now just 80 minutes away from playing the final at the Millennium Stadium.
"The semi final is a great chance for us as the prize of winning is playing at the Millennium Stadium - our national pitch and whatever anyone says the magic is still there. Certainly as you progress through the last 16 and get a quarter-final spot it's something everyone at the club talks about."