The World Cup final already had an electric atmosphere but, when Mandela appeared, the excitement rose to fever pitch.
"We were standing there in awe. There's just something about him. It's a presence. You can just feel it straight away. There's something special about the man."
Like his fellow team-members, 24-year-old All Black Josh Kronfeld got to shake Mandela's hand. But Kronfeld was focused on the game, which South Africa won 15-12, and it's only in hindsight he realises the significance of the moment.
"At the time I didn't put much thought into it. I was playing rugby, you know?
"I look at it now and think what an amazing treat to meet him."
Kronfeld said it was a shame that Mandela's incarceration meant the world didn't have longer with him.
"He had such a small window. He did make the best of it. It's just a shame that it wasn't for longer."
One of Mandela's strengths was his understanding that sport could be used for good.
"Sportsmen often try to segregate politics from sport but, unfortunately, they don't stay separate. We've seen that in history over and over. But he saw the usefulness of sport bringing the country together."
Mains went on to coach South African rugby teams the Lions and the Cats.
"I was fortunate enough to meet him and he was such a lovely, humble man. He's a model human being; an icon that the human race needs to be proud of.
"To go through what he went through and to come out such a balanced leader for South Africa, personally, I think it was one of the great achievements for a human being of our time."
Mains said Mandela had left his mark on the world in the right sort of way.
"If a few other people around the world could have the compassion and balance that he's got the world would be a much better place to live in."
Mains' wife, Annemarie, who is South African, said Mandela knew how to connect with people from all walks of life.
"I think everybody's expecting him to die, but I don't want to go there yet."