Perry, an abortion opponent, said his biggest concern had been Giuliani's support for abortion rights but that he was satisfied Giuliani would appoint judges who view the issue conservatively.
"The one (issue) that I wanted to hear him give me an answer and look me right in my eyes was that issue of who can I expect, what type of individual can I expect on the Supreme Court," Perry said at a news conference with Giuliani.
"He clearly said ... you can look for people like Scalia and Roberts and Alito. Let me tell you, I can live with that," Perry said, referring to conservative Supreme Court Justices Antonin Scalia and Samuel Alito and Chief Justice John Roberts.
Giuliani, who is addressing social conservative voters this weekend in Washington, said he wants conservatives to focus on areas where he agrees with them.
"I'm not going to get every vote," he said. "The idea is going to be that there's enough we agree about and enough we're facing - foreign threats and domestic problems - that it may just be if they think about it, that I'm the best candidate."
"What I really want is a relationship in which we respect each other, even if we disagree," Giuliani said.