I think the best thing is to offer as much reassurance as you can to reduce the anxiety and wait it out. A comforter or special toy may also help, as Trish suggests.
If you leave her at night, do you try "I'm just going to x and I"ll be right back"? Then come back obviously. Adn do it again and again, till she's secure in teh knowledge that you will come back and goes to sleep (it takes a while for this to work)