Saint struggled to comprehend the attention Grant attracted when the pair went to see a show during a break in filming their 1959 Alfred Hitchcock thriller.
And the Oscar winner admits the outing made her feel fortunate to be able to live a normal life.
She tells Vanity Fair magazine, "A buzz went up in the audience the moment he (Grant) was recognised. It was like a wave of adulation rolling round the theater. I found it overwhelming and a little scary. I was thrown by it. And I asked him, 'How do you handle this, because I know I couldn't?' It was almost as if he were talking about someone else when he said, 'They'll tell their friends tomorrow that they saw Cary Grant. It makes them happy!'
"I know I couldn't have coped with that kind of fame. And I've never had it - thank the Lord! People recognise me, but I wanted a normal life. I remember when I was with Elizabeth Taylor and Richard Burton on The Sandpiper - they were so famous they couldn't go anywhere."