I've done it once a few years ago.
If it's an antique it's legally a "non firearm" in both countries. No import or export permits needed.
USPS regulations prohibit shipment of regular firearms, but their regulations do allow them to ship antique firearms.
I put "pre-1898 antique" on the customs declaration and my own home made antique letter in the box with the gun where it would be found if the package was inspected. I also included a copy of the receiver's FFL - which may not have been required but since he had one we stuck it in the box anyway. My letter contained the make, model, caliber, s/n, and date of manufacture, and states that it is antique and legally considered to be a non-firearm in both Canada and the USA. Then I stuck it in the mail and two weeks later it arrived at the destination. It had a sticker saying it had been opened by US Customs Services.
I've heard of Canada Post refusing to ship firearms outside Canada. Seeing that an antique is legally a non-firearm this shouldn't be a problem but apparently it has been for some people. If you call it a gun, then it is a gun. If you call it a pre-1898 antique then it's a non-firearm. YMMV.