My 4 year old daughter (also Emma =)) does that occassionally. We usually cannot wake her up and if we try to interfere, she gets more upset. I've had the most success just picking her up and hugging her, rubbing her back, etc. to soothe her back to sleep. She is very sensitive, so some one elses suggestion of something bad happening that day could be a possibility.
My parents said that my brother did that when he was a baby (very often and would walk around - scared them a lot) and the only way they got him out of it was putting him in front of the TV or turning on music. I guess that got his mind to something else. He would wake up and go back to bad. We haven't gotten to the point where we've tried that yet.
That's all I've got. I'm curious to see what other advice you get. Good luck!
B.