Ginsburg remembered her "best buddy" as someone who both revered the Constitution and the Supreme Court.
"Justice Scalia once described as the peak of his days on the bench an evening at the Opera Ball when he joined two Washington National Opera tenors at the piano for a medley of songs. He called it the famous Three Tenors performance," she said in a statement on Sunday. "He was, indeed, a magnificent performer. It was my great good fortune to have known him as working colleague and treasured friend."
During a joint appearance with the woman he also has called his "best buddy" on the bench, Scalia said, "Why don't you call us the odd couple?"
"What's not to like?" Scalia joked at the event hosted by the Smithsonian Associates. "Except her views on the law, of course."
The two justices and their families vacationed together. There was a trip to Europe where Ginsburg went parasailing, leaving Scalia on the ground to admire her courage but at the same time worry she might just float away.
In her chambers, she has a picture of them riding an elephant in India. Ginsburg -- the pioneer of gender equality-- has said that she was only sitting behind Scalia to distribute weight more evenly on the elephant.
Ginsburg's late husband, Martin Ginsburg, was a gourmet chef, and the two justices often spent New Year's Eve together celebrating with their spouses.
They never shied away from the fact that they didn't often agree in many opinions.
It was Ginsburg who wrote the landmark 1996 case, United States v. Virginia. The opinion struck down the all-male admissions policy at the Virginia Military Institute. Scalia dissented, but he offered her an advanced look at his dissent in order to improve her majority opinion.
She often said that having the dissent ruined her weekend but made her final product better.
They disagreed on same-sex marriage and wound up on opposite ends of the case. Ginsburg welcomed the swift change that swept across the country and brought the issue to the Supreme Court. Scalia believed fervently that the issue should be decided by the people, not the courts.
He wrote a biting dissent when the court cleared the way for gay marriage last spring.
"The issue is quite simply who decides, that's all," he said at the Smithsonian event.
But he respected Ginsburg for the kind of judge she is, offering clear and concise guidance to the lower courts.
"I love him, but sometimes I'd like to strangle him," Ginsburg once said, according to Reuters.
As close as their friendship was, they never went duck hunting together. Justice Elena Kagan got that honor. After she joined the court, Scalia taught her to shoot. They started out with clay pigeons and later moved to deer, antelope and ducks.
Scalia frequently appeared at events hosted by the conservative Federalist Society, where he would be greeted with a standing ovation. Once he brought all nine of his children on stage with him.
Ginsburg's standing ovations come from the more liberal American Constitution Society. Last Friday she went to the ribbon cutting of the new law school at American University, praising the school that had been founded by women.
"Brilliant thinkers, they loved a good joke, the law and opera," said Arnold & Porter lawyer Lisa S. Blatt, a former clerk of Ginsburg.
Blatt, who argues frequently before the court, often found herself the recipient of tough questions from both justices.
"They had the world in common," Blatt said.
Scalia was also the subject of a one-man play, "The Originalist, " recently at the Arena Stage theater in Washington.
Actor Edward Gero did an uncanny job in capturing Scalia's mannerisms. Scalia took it all in stride, referring to it as the "age of celebrity" and telling the Smithsonian audience he would not be going to see the play.
But Ginsburg revealed his more personal side, noting that he had gone out of his way to have lunch with Gero. He also invited him to oral arguments.
Ginsburg and Scalia were also the subject of an opera, "Scalia/Ginsburg," composed by Derrick Wang. It had its debut last spring.
At speaking events, Ginsburg often delighted in reading excerpts from the opening aria of the Scalia character: "The Justices are blind! How can they possibly spout this/The Constitution says absolutely nothing about this."