Swansea will face fierce local rivals Neath in an all-Premiership derby at St Helen's in the quarter-finals of the Konica Minolta Cup.
Pontypridd, who lost in last year's final, also have a home draw against Division One side Builth Wells - the only remaining non-Premiership team.
The remaining two ties see Llandovery travel to take on Cardiff, while Maesteg will host Newport.
The matches will be played on the weekend beginning 1 April.
Although Builth Wells are the weakest side in the draw on paper, Pontypridd head coach Simon King said they will be taking nothing for granted.
"Any team left in the Cup at this stage deserves to be there and we are just delighted to be at home in the quarter-finals," King said.
"We will give Builth Wells all the respect they rightly deserve as they are a proud club with a proud cup tradition and we are already looking forward to the day.
"As far as we are concerned we want to put the record straight after the disappointment of last season's final and we also have a fine cup pedigree.
"We have got a young side and the closer we get to the final the better it is for these young players to get quality experience of the big-game atmosphere."