In Michael Clayton, Tilda Swinton plots to kill George Clooney. In real life, she's much nicer, though she does fantasize about blackmailing her costar. "He has to be in every film that I'm in," says Swinton, 47, who jokes that "I'm holding an incriminating photograph of him." So far, her extortion plot is working: Her next movie is Burn After Reading, also starring Clooney. "He's got so much energy," she says. "It's great, great fun to be around him."

If only her Supporting Actress nomination for Clayton—as a ruthless attorney who will stop at nothing to stave off a multimillion-dollar lawsuit against her company—inspired the same enthusiasm. The London-born Swinton, who lives just outside Inverness, Scotland, says she's never watched the Oscars and "can't think of many more terrifying things" than walking onstage to accept the award. "It's such a magical mystery tour for me," she says. "I'm quite looking forward to it, but I don't know what to expect."

Nor has Swinton decided whether to attend the Awards solo or take a date. She still lives with her ex, artist John Byrne, 68—the father of her 10-year-old twins, Xavier and Honor—though she has been dating German artist Sandro Kopp, 29, for three years. "It's not that exotic, really," says Swinton. "[The children] are the center point of everything." And what do her kids think about Mum being a first-time nominee? "They're oblivious," says Swinton, happily. "They don't even know what an Oscar is!"

  • Contributors:
  • Monique Jessen/London.