1. Andrew wanted to ask Gail to marry him but he couldn’t find the words. He stood there, hat in hand, hemming and hawing.
2. You don’t have to be afraid to tell me what happened. Stop hemming and hawing and get to the point.

Compare to: beat around the bush; stonewall. Similar to: hum and haw. The expression probably originates from the sounds one might make when clearing one’s throat and trying to introduce a delicate subject.