Hi Mark, we have a sharpening service that picks up and drops off on Thursdays before the store opens. They do sharpen hand saws at $20 per saw, but can only do a saw with up to 13 teeth per inch. Most mitre box saws have a really high tooth count and would be too fine for them.
I would give them a call or go into the shop and ask. If they don't I am sure they will direct you where to go.
Thanks! Your answer is awaiting moderation.