Watts plays Plame in Doug Liman's upcoming movie Fair Game, which explores the personal and political fallout which occurred when the covert spy's identity was leaked to the media.
"She wanted to meet at an airport," Watts told Metro. "I remember saying to my husband, 'Who on earth meets at an airport?' And then I thought, 'Oh yeah, of course. Spies do.'"
The pair eventually met at a New York restaurant and Watts added: "I was a bit embarrassed at that first meeting. I was so respectful of Valerie that I thought, 'Oh no, she's going to think I'm a total dumb arse so I'll just go carefully and slowly with her'.
"It wasn't until our third meeting that we ordered a nice bottle of wine and I felt like I could throw some really personal questions at her, like how did she deal with this in the home? How did it affect her family and marriage?"
> Click here to read our review of Fair Game