Mention the words film and premiere and it's amazing how many people go weak-kneed and start cooing about "glitz" and "glamour"; journalists who report on them tend to be less starry-eyed. They have generally spent a lot of time standing and waiting in a pen, sometimes in the rain, praying they will be able to identify "the talent" in the passing traffic of bow ties and designer gowns.

They line up beside the red carpet, microphones primed, in the hope that the most photogenic actors will pause to shower them with something quotable, like royalty dispensing coins to the hungry groundlings. The one thing they generally won't get is to see the film.

It's not every day you see Winnie Madikizela-Mandela at a premiere, but that's what happened last week. She was in Johannesburg for the opening of Invictus, Clint Eastwood's take on how Nelson Mandela turned the 1995 rugby World Cup into balm on the wounds of apartheid. Mandela is played by Morgan Freeman, while the role of the South African rugby captain, Francois Pienaar, goes to Matt Damon.

This time, the carpet was yellow, instead of red, at the behest of a mobile phone company. The venue was Emperors Palace, a pleasure dome and casino that could be in Las Vegas, or on the moon, or in fact anywhere but Africa.

A small crowd gathered to watch the entrance of actors and former rugby players reserved the biggest cheer for the imposingly tall, earstud-wearing Freeman.

For an actor, Mandela is surely the King Lear of non-fiction roles. He is a man who has been all but sanctified in his own lifetime, and any attempt at impersonation could seem like meddling with a myth. At least Gandhi was dead when Ben Kingsley performed his act of impertinence.

Freeman moved along the line of waiting journalists, and my turn came. I found him to be a man of unflinching pithiness. First I asked him to define the key to such a momentous role. "I'm not sure," he said. "I think maybe my height."

He laughed. I laughed and asked: "And the accent?" The actor replied: "Well, if you could get that ... I don't know if I got it or not, but if I did, that's one of the keys. Trying to get as much of him as possible, working at him from the inside out, the best I could."

I wondered whether it had been daunting. "Once we got started, no; but thinking about it, yeah."

So, I asked, how important was Mandela's gesture in throwing his weight behind the South African rugby team, traditionally favoured by whites and hated by blacks? Freeman replied: "Where are you from?" I told him and he said: "You should ask the South Africans, do you know what I mean?"

He moved along the line and spoke to more journalists. A lady from the Associated Press asked him how he had prepared for the role. "I studied," he said.

Journalist: Did you meet with Mandela to prepare?

Freeman: Lots of times, yes.

Journalist: What was it like?

Freeman: Did you see the movie? That's what he was like.

On this occasion, I had seen the movie, and was held from start to finish. Freeman, who has grace and gravitas in spades, gets many of the mannerisms and expressions right, particularly Mandela's posture and gait. More importantly he embodies the effortless regality, wily pragmatism and magnanimity of the man, along with a shot of melancholy at his heart.

In one scene, the almost all-white Springboks team takes a boat trip to the former apartheid prison on Robben Island. Pienaar steps into Mandela's old cell and pulls the door shut after him. He stands in silent contemplation of the tiny space. Outside, in his mind's eye, he can see Mandela in chains, breaking rocks. When Freeman looks up from his labours, it's not quite possible to put The Shawshank Redemption out of your mind, but the present dissolves into the past.

Sporting films have a natural trajectory towards an ending of tension, euphoria and catharsis. South Africa win the World Cup and Mandela's shrewd investment in cultural symbolism has paid off. Standing outside Emperors Palace, I asked John Carlin, the British author of the book Invictus is based on, why he regarded it as such a masterstroke.

First, Carlin argues, Mandela used sport to turn black people away from vengeance and resentment and towards reconciliation. Second, he was able to persuade white South Africans they had nothing to fear from his presidency.

Carlin, who reported from South Africa from 1989 to 1995 and met Mandela often, told me: "When he left prison in 1990, most white South Africans thought the government was completely mad because they had been programmed to regard him as a great communist terrorist – South Africa's Osama bin Laden. In the space of five years, Mandela manages to turn that around to the point that practically the whole of white South Africa crowns him king at this rugby World Cup final."

What would the Mandela of 1995 make of the South Africa of 2009?

Carlin replied: "I think he'd have mixed feelings. I think in South Africa, to take a strident view one way or the other on what has happened here and say it's all gone terribly wrong or fabulously right – both are ridiculous, silly, immature conclusions to reach."

On the one hand, Carlin said, there is a sense of nationhood, political stability, rule of law, freedom of the press and solid democratic structures. On the other, there is corruption, criminality and failing service delivery to the poor. He described the former president Thabo Mbeki as "a disaster, a catastrophe". He added: "Mandela shares that view, I know."

But the journalist of 27 years finds more to admire than despise here. "Look where we are right now. There's a splendid casino/emporium type place; there's a highway right here with cars rushing past. This is not Afghanistan. The point is that South Africa, when I was here, seemed to have the distinct possibility as emerging as Afghanistan, as just becoming a wasteland.

"The words 'civil war' were in the minds of a lot of people. Certainly, there was a prospect of a hell of a lot of violence and the country really falling apart. But 20 years after my arrival here, South Africa remains a stable country and is about to host the biggest public event in the world – the football World Cup."