I used to put Elvis in his carrier rather than crate Cassidy. She had severe barrier frustration, and was very leash reactive, so putting her on leash in the house or crating her with the cat loose just sent her over the edge. And that of course freaked out the kitty, making things so much worse. She'd go off, and he'd run out of the room. So I started bringing her into the cat room for daily visits (he stayed in there for the first couple of months so their only interactions were controlled visits with me present), and I kept her calm, sitting on the floor with her while she chewed a special cheese filled bone that she only got in the cat room. Elvis could safely observe from his cat tree, and even come down close enough that they could sniff noses.
Sometimes he'd stay up at the top of his tree, so I wouldn't be making any progress in getting them used to being in close proximity. I'd let Cassidy out of the room, get Elvis down and put him in his carrier and set it on the floor. I'd bring her back in, and she'd lay down in front of him where they could see and sniff each other while she chewed her bone. Since Elvis was a kitten, he was somewhat afraid - she was around 80 pounds and he was the size of her head, but also interested and curious. For a totally terrified cat I don't know that I'd do things that way, but it worked well for me with Cassidy and Elvis. It's really important to keep the dog calm and preferably laying down so as not to be intimidating to the cat. You don't want a dog jumping up and down and barking at a cat in a carrier, this is a controlled situation where everyone is allowed to hang out and get used to each other. Feeding everyone treats at the same time is good too. I used cut up Natural Balance rolls and also jerky treats in tiny little pieces, and both cat and dog loved them.