But they generally squirm for a few seconds then become resigned to the fact that you've got 'em.
It's terrible because you can often feel their little hearts racing.

Be prepared for nipping. Some will nip. It doesn't really hurt per se, but it's not comfortable, as those beaks can be sharp!
Quick funny story: My weaver, when I got her at the store, had really long nails, so we went around, gathered the supplies to clip her nails and then clipped them in the store before we boxed her. Well, the entire time, she had her jaw clamped on the sales girl's finger, often doing a gnawing motion! She was one pissed off little bird, that's for sure!
But indeed, they usually squirm until it becomes clear you've got them. Then they act more like a cat who's scruffed.