Miriam, 81, acted alongside Dame Maggie in the Harry Potter movies, where she played Professor Sprout, and Dame Maggie played Professor McGonagall.
Speaking of Dame Maggie, Miriam admitted that she is “a very sweet lady”, but that she can be “a bit alarming” if you get on the wrong side of her.
Elsewhere, Miriam has also confessed to being scared of Dame Judi Dench – who “doesn’t suffer fools”.
The trio of some of the country’s best actresses all starred alongside one another in the 2005 film Ladies in Lavender.
Miriam later admitted that she found Dame Judi to be terrifying.
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She said: “I was a bit foolish and it was when we were doing Ladies in Lavender, it was her and Maggie Smith and me, and let’s face it, that’s a bit scary.
“I worked with Judi Dench and she is not a bit relaxing, she is terrifying.”
“She is very direct and she doesn’t suffer fools.
“I didn’t know what to do and I sat there in the room, and said: ‘Shall we talk about acting?’
“And I think they thought that was a bit b****y stupid. Maggie Smith said, ‘No, let’s not’.”
Miriam also said of Dame Maggie: “She is a little bit alarming.
“You have to be watchful with Maggie because if she’s cross, she doesn’t mind sharing it.
“She’s actually a very sweet lady and if you don’t irritate her she’s absolutely gorgeous.”
However, the pair must have a close relationship as Miriam commented on how the death of Dame Maggie’s husband had a deep impact on her in a revealing documentary.
Speaking during The Marvellous Maggie Smith: A Celebration documentary, Miriam said: “I never met Beverly Cross, but I know that he adored Maggie,” she explained.
She added: “[I know] that he was wonderful to her, that he took care of her.
“And that she loved him very much, and she was utterly stricken when she lost him.”
The Harry Potter star went on to conclude: “It was awful.”