The Tipperary men will be looking to maintain that form and build on their impressive 9-5 AIB Cup first round victory over Lansdowne back on September 27.
How important will home advantage be remains to be seen, but Barnhall will travel with renewed confidence after breaking their duck last time out in the league.
The Kildare side accounted for Banbridge on a 9-3 score-line but, like Nenagh, they only boast one win in four league games so far this season.
The winners of Saturday's clash, the meeting of the 12th and 13th-placed teams in AIB League Division Three, will be away to Galwegians or Highfield in the third round.
Writing on the club's website, Nenagh Ormond prop Fergal Brislane said: "After the felling of Lansdowne, lets hope we can maintain the run of cup form and possibly earn ourselves another big day out.
"This is a team with a much similar run of form to our own, however, and they certainly cannot be taken for granted. I hope also that you, our supporters turn out in numbers.
"Cup rugby is always tough and even tougher with poor support so lets see you all there Saturday and help create some more of the atmosphere that is still ringing in Lansdowne ears.
"For us players it is important to kick on after ending our poor run with that win over Queen's. Its time to build momentum for the return of the league in a few weeks and no better way to do that than a cup win."