As someone who has done this before - I bought a 1730's French Liege Made pistol from Thomas Del Mar. The Auction House is world known and was incredibly polite and helpful as they could be,... I stress could be. In other words, all they could do is give me the name of some local packers and shippers to try.
For that pistol I got 5 responses. 3 said "it's a gun we won't touch it no matter when it was made - even 1730". I tried "Can you take the lock out and ship in 2 boxes". "No" was the answer, "just the barrel is listed as a deadly weapon, and we will not ship it". Two quotes came back at $1200+ and $1600+. Yep - around US $1500 to get a flintlock pistol here.
Now I did call gun dealer friends who put me in touch with a fine shotgun dealer here in the US. He does about 4 shipments a year - bulk. I was able to get a shipper from him who would pick up, pack, and ship for $680 dollars. I was ready to have the auction house keep the gun and resale for me. So I went with the shipper charging the $680 - I was lucky because they don't ship often - only about once a month. I was close to ship date - about 1.5 weeks. Still, everything from the shipper got hung up - the whole shipment - so it was delayed by 6 weeks, and this is BEFORE Covid.
I also took a friend's advice and paid $185 for a customs broker here in the US. Thank goodness I did, or I probably would still be trying to get the gun. The paperwork is heavy and if 1 letter or period is suspicious or out of place and you can forget it.
I still had to drive to the airport over 1 hour away and pick up the pistol from the huge FedEx warehouse (they were the carrier). I was there for 2 hours while they hunted it down and went over all my customs papers.
In the end I did get a beautiful gun for about what it would sell for here through an auction, but I added a lot of stress and hassle.
I would NOT TRY to get a long rifle to the US unless I had a best friend in the shipping or bulk gun exporting business that would help me and let it piggyback in their bulk shipment - still add 50% on to the hammer price just for shipping and fees.
UK Auctions also charge enormous fees, including VAT tax - so hammer price, plus buyer prem, plus VAT, plus shipping you will double the final price or more.
I have tried many angles to get to great arms in Europe, but it's getting almost impossible. Germany is the easiest - I bought an early 1600's WheelLock rifle and the seller (dealer) paid my shipping and handled customs. It was smooth but did have a few US customs hiccups that required me fill out 2 more forms. About 6 weeks delivery time total.
Swords have never been a problem for me - but I have not bought one in 3 or 4 years. ByGoneBlades is a super dealer - last I dealt with.
Take my word - just get the thought out of your mind unless you know the piece is a rare, one-of-a-kind, rifle that has to be retrieved at any cost. Then plan 6 months to a year and a LOT of money and hassle.