WASHINGTON — President Bill Clinton, who put Justice Ruth Bader Ginsburg on the Supreme Court in 1993, joined the justice on Wednesday for a public conversation. So did Hillary Clinton, the former secretary of state, who might have named Justice Ginsburg’s eventual successor had she won the 2016 presidential election.

The conversation, at Georgetown University Law Center, focused on what the participants said was a radical change in federal judicial nominations. Mrs. Clinton, without naming names, said the Trump administration has been appointing unqualified judges.

“We’ve seen people largely chosen on the basis of age, and therefore longevity, and political ideology being pushed through despite having no relevant experience,” she said. “Before the last several years people took seriously the selection of judges. Even if they were trying to find somebody who would get to the result they wanted, they wanted to be able to say that this was a distinguished lawyer, that this was a judge with experience.”

By contrast, Mr. Clinton said, he was taken by Justice Ginsburg’s career as a pathbreaking women’s rights litigator when he was considering her for the Supreme Court. He said he was also struck by her forthrightness when they met in 1993 for an interview.