I've been traveling to Canada to shoot in the National matches held outside Ottawa for 20 years.  US residents have the same type of paperwork to prove the article originated in the U.S.
The paperwork is Form 4457 Certificate of Registration for personal effects taken abroad.  I've always filled out the form on the U.S. side before crossing the boarder.  I believe it can be done at most Federal custom agency offices in major cities.
Without this piece of paper, customs can confiscate, fine and/or demand an importation tax be paid.  I have a stack of these certificates where camera's, spotting scopes and rifles along with serial numbers are listed.

I was given a cedar canoe as a wedding gift while in New Brunswick.  I had to pay the importation duty on it based on a value the customs agent and I agreed upon almost 40 years ago.  Since then I've made sure to register anything of value when going out of country.  Frank M.

Back about 30 years ago I was working for the USGS in Anchorage Alaska.  We were operating a seismograph in Kulane Lake Yukon Territory.  I was sent down there to remove and bring it back to our Anchorage office.  I was driving a US Government vehicle with GSA plates on it and the instrument I was bring back had USGS property tags on it and was also marked by the manufactures as being make in Garland Texas.  The US Customs agent informed I would have to pay duty to bring it into the US even though It was plainly marked as US property.  I argued with him and finally he called his supervisor and they finally let me proceed with the understanding that I was to bring the items to the US Customs office in Anchorage within one week.  I did that and did not have to pay their duty.