"It's very meaningful mostly to have a friend officiate, and then for someone of her stature, it's a very big honor," Kaiser said. "I think that everything that's going on that makes same-sex marriage possible and visible helps to encourage others and to make the issue seem less of an issue, to make it just more part of life."
Ginsburg released a statement Friday, citing her friendship with and admiration for Kaiser as the reasons she officiated at the union.
Ginsburg reportedly has another ceremony planned for September.
Justices generally avoid taking stands on political issues. The wedding, though, comes after the court's landmark ruling in June to expand federal recognition of same-sex marriages, striking down part of an anti-gay marriage law.
Same-sex marriage is legal in the District of Columbia and 13 states.
ABC News and the Associated Press contributed to this report.