"I was so engrossed with her story when we were sitting there that I suddenly felt that I was not interviewing someone for the Supreme Court at all," Clinton recalled, "I was just a guy talking to somebody I really liked and that I hoped would be part of our future."
For her part, Ginsburg volunteered that she was surprised by how "very easy" it was to talk to Clinton.
"I've had the experience with some men that they have some discomfort talking to a woman," she quipped. "It was not that way talking with President Clinton."
The crowd erupted into laughter.
Ginsburg, 86, spoke in Little Rock, Arkansas, at an event organized by the Clinton Presidential Center. It marked her third high-profile public appearance in less than two weeks since completing radiation treatment for a localized malignant tumor on her pancreas.
"I'm pleased to say, I'm feeling very good tonight," she told the crowd.
Clinton nominated Ginsburg in June 1993 to replace retiring Justice Byron White. She was later confirmed by the U.S. Senate 96 to 3, becoming the second woman ever on the high court bench.
"I liked her, and I believed in her. I just knew she was the right person for the court," Clinton said while introducing Ginsburg. "But I have to say in the last 26 years she has far exceeded even my expectations."
Ginsburg has reached near rock-star status among Democrats for her landmark opinions advancing gender and marriage equality and defending the civil rights of immigrants and people with disabilities.
"One thing I did not see coming is her ascendance to pop culture icon," Clinton joked. "Now you can see her image on T-shirts, totes, coffee mugs the world over. You can become resentful of such a person, but … we like her because she seems so totally on the level in a world hungry for people who are not trying to con you, who are on the level."
The 73-year-old former president also suggested that he has tried Ginsburg's much-publicized workout regimen.
"Her workout routine is marveled at. Hillary got me a book: 'The RBG Workout.' And she said, 'I bet you can't do it.' I said, 'I'm 73. I'm just a kid. I can do this,'" he recalled.
Asked how she keeps going at her age, after several bouts of cancer, Ginsburg credited her job.
"I think my work is what saved me," Ginsburg said. "Instead of dwelling on my physical discomforts, if I have an opinion to write or brief to read I know I've just got to get it done and have to get over it."