The 30 Rock star plays the sleazy husband of Blanchett's depressed leading lady in the film and he admits it was a thrill to act alongside her.
As a result, Baldwin has become her champion and cheerleader as his co-star attracts Oscar buzz.
He says, "To be on a set with someone like Cate, who is probably one of the five greatest movie actresses of her generation, I watch her put herself through that - it was a very, very emotional and kind of idiosyncratic role - and watch her and Woody collaborate. She would do it again and again and again.
"I hadn’t been around that in a while. I was overjoyed to be around her. Cate is so wonderful in this film. I often hear people talk about Oscars and Oscar predictions with films and that kind of rubs me the wrong way but, in her case, I really do think she probably will get nominated for an Oscar for the film because she’s so wonderful in it."