Contepomi scored six penalties during Leinster's 21-12 win over Munster on Saturday to take the Irish Province one step closer to securing the Magners League title.
But Edinburgh knocked Leinster out of the Heineken Cup at Murrayfield in December by nullifying the attacking threat of the Argentina playmaker and Godman revealed his side will be targeting a repeat performance at the weekend.
Godman said: "It should be a good match-up. I enjoy playing against Contepomi; we are slightly similar players.
"He is a class act and he can produce something out of nothing. When he is on form he is hard to stop. He is one of the best around, so we need to stop him playing on Friday night.
"Our defence was fantastic during the win against Leinster in the Heineken Cup and we need to get back to that, especially after our last two performances.
"That was a brilliant display and we will need to replicate that because they have got some world-class players in their team. We will have to step up and put pressure on them."
Following the disappointing derby defeat at Glasgow, Godman revealed the Edinburgh players were frustrated by their below-par performance.
But he is adamant the team is refusing to panic over recent results and insists they are not far away from returning to winning ways.
Godman said: "We have got to look at a couple of things, but to be honest there is nothing major.
"We have to regroup this week and we've got to get the show back on the road. We've got our final home match this Friday and then we've got two tough away games; we want to finish this season as well as possible."
The Scotland internationalist also welcomed the club's initiative to reduce admission prices for pre-booked Adult tickets (from £15 to £10) designed to reward the loyalty of the club's supporters and to also encourage newcomers to sample the Edinburgh match experience.
He said: "It was great to see so many Edinburgh fans at the Glasgow match and the noise they made was noticed by the team.
"It would be great to see another big crowd at Murrayfield on Friday because we want to finish the season on a high note and give them all something to cheer about."
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