Due to mixing up a street in Los Angeles with one in Orange County, 26 miles away, the actress from Canada was horribly, grotesquely, bizarrely tardy– so late that the British director gave up and went away. Yet she still got the part in Beetlejuice. In Burton's world it pays to be different.
"It was a good thing I missed that meeting," she laughs. "I might have blown it. Something about me being late made Tim want to work with me."
It was the start of a working relationship that has gone from 1988's Beetlejuice to 1993's The Nightmare Before Christmas and now Frankenweenie, a typically Burtonesque, beautifully animated tale of a boy and his dog that had its premiere at the London Film Festival last week and is now on general release.
O'Hara, 58, gives voice to three characters in the film: Mrs Frankenstein; a gym teacher; and, much to her delight, a gloriously lugubrious concoction called Weird Girl.
"What fun to try to play a kid, first of all, then Weird Girl is just perfect because you know how the rest of the world sees her, and it's right away fun to imagine she in no way sees herself that way, and has no idea what impression she is making. That's true of most of us I think."
O'Hara makes a multi-faceted, cut-diamond kind of impression on the world. For starters, there is the side of her that's Catherine O'Hara, star of the blockbuster Home Alone. Then there's Catherine O'Hara the killer improviser and jewel of cult comedies A Mighty Wind, Best in Show and For Your Consideration. Add Catherine O'Hara the Burton heroine, Catherine O'Hara the writer and Catherine O'Hara the mother (to two children), and you have a happy jumble, for which growing up in Toronto, the second youngest of seven children, proved to be good training.
"The way to get attention in our home was to get a laugh, have something to say – quickly, really quickly." Her parents encouraged their children to talk about their day, with mum and dad joining in too, dad telling jokes, mum re-enacting incidents.
O'Hara also had a talent for impersonations. "I'm kind of a monkey that way," she says. Her repertoire started with mostly men – Alfred Hitchcock, James Mason – before moving on to Carol Burnett, Lily Tomlin and Katharine Hepburn.
In creating the voice for Weird Girl, O'Hara started with an illustration, then heard a little of the character's story and some of the dialogue. Drawings and figurines were in the studio too and were great inspiration. After that, it was up to her to give life and shape to the characters through their voices.
A film about grief and monsters and the infinite power of science might not sound like typical family film territory, but Burton has made his reputation on confounding expectations. O'Hara disagrees with those who would categorise his work as gloomy.
"Life is dark and light, 50 lights and darks in a day for most people, and sometimes more of one than the other. It's a way more honest representation of life if you are mixing the light and the dark, and he blends them really well. He's got a childlike innocence in the way he lets himself see things for the first time and presents them that way."
When they finally did get together to shoot Beetlejuice, O'Hara and Burton immediately clicked. She liked his sense of humour, the way he looked at the world. Far from the film being a walk on the wild side of weird, she felt right at home and adored the character of Beetlejuice, the "bio-exorcist" played with gleeful devilment by Michael Keaton.
"When I read [the script] I was completely wrong in how I pictured the character of Beetlejuice. I pictured some old, lecherous character. Good thing I wasn't directing," she laughs.
She has another reason to think fondly of Beetlejuice and Burton, because it was the British director who played matchmaker and encouraged Bo Welch, his production designer, to ask O'Hara out. Their children are now 18 and 15.
Two years after Beetlejuice, O'Hara was cast in Home Alone as Kate McCallister, the mother who manages to leave her son (played by Macaulay Culkin) behind at Christmas. It was a hit on a par with Slade's Merry Christmas Everyone, earning $476 million worldwide at the box office and giving rise to several sequels.
O'Hara has fond memories of that time. "It was really happy, especially the first one because there was more innocence about it, it hadn't become what it became and the second one was bouncing off the monster success of the first. For the most part everyone handled it well. It was still fun but it was less innocent in a way, just has to be."
A large part of the films' success was down to the "cool" kids cast by director Chris Columbus. "Macauley was just this beautiful little odd boy, a kind of freak of nature, with this beautiful little face, just a sweet presence."
Though O'Hara drew the line after the sequel, the film went on to have several more reprises. Even doing two films was pushing it, she felt, noting: "There would have to be a prison term for those parents."
It was not a role that could be that easily left behind, however, as an encounter with a young fan demonstrated.
"I had a child about eight years old come up to me in a mall once. He said, 'You're the one who left your child.' Yes, I said, I was in a movie where I played someone who did that. 'No, you left your child and you did it twice.' Yes, I said, I did a sequel to the first movie."
The kid would not let it go. "He said, 'Isn't that called abandonment?'" As O'Hara tells the story her face and voice click through lots of permutations, like a movie projector on fast forward. She's fast and funny and you can see why she became part of the improv crew assembled by Christopher "Spinal Tap" Guest for such mockumentaries as Best in Show.
To O'Hara, Guest's films are another happy jumble in which a shoot of 90 hours ends up being a 90-minute film, but there's a lot of discipline there too. While the dialogue might be improvised there's a structure to each scene, points that have to be hit. The golden rule, of course, is to leave the audience to do the laughing and not burst into giggles yourself. That, says O'Hara, would sabotage a scene for someone else. "Everyone is really into the job," she adds.
It's not always easy, though. In one dinner party scene she had to pretend she had dropped something on the floor so she could duck under the table to hide her laughter. "You don't want to kill the scene."
For O'Hara, funny woman and Weird Girl, that would never do.
Frankenweenie is in cinemas now.