If you're buying a vintage mitre box then hold out for one that comes with its original saw. Lie Nielsen will make you a saw to custom fit any mitre box but it'll be expensive.
I picked up a decent 1960's Craftsman mitre box with the saw for $8 at a consignment store.
Unless the box is the type of affair that is a U shaped channel with kerfs at 90 + 45, then the dimensions of the saw will need to match the box in some way generally. Usually in plate thickness, or depth from spine to teeth, or size of the spine. Trying to find a backsaw that meets the criteria for a random mitre box may take you awhile.
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