Most studies looking at pellets (the fur and bones remaining from eaten prey that an owl will regurgitate, often before flying off to hunt again), show that small rodents make up a high percentage of the NSWO diet. You can imagine how great it is to have a rodent hunter like a saw-whet around! This photo is a pic I took of an actual NSWO pellet.
NSWO, Cannings 1993, but you can go and subscribe online to this excellent resource!
Sometimes these small owls can't eat their whole prey, and eat them in pieces. If their is too much for one meal they will either cache the leftovers somewhere safe, like a crook in branch, or they will roost on top of it. What better way to have a warm dinner?