I just returned from the UK with 5 antique shotguns (pre-1898). It was a first time for me, so I asked friends and my RFD about the best way.
I used an SKB hardcase (for golf clubs $79.00 on sale)to transport the guns. It meets the requirements of locked/hardcase. It attracts a lot less attention than a standard gun case. The guns were protected in bubble wrap inside. I used a strong bicycle lock around the case in addition to the lame latch locks.
You are limited to 50lbs/23kg per bag now. The SKB case was 21.5 lbs empty. I weighed a pair case at 14 lbs empty. That was over 2 guns of weigh, so no cases came back.

-Have copies of the bill of sale, include serial numbers and appox date of each gun with the documentation of age.
-Keep a copy of paperwork on outside of luggage and with you.
-Your UK registered firearms dealer (RFD) must escort the guns with you to the airport or meet you at the airport with the guns.
-Let your airline agent know you have antique guns. I used the term "disassembled antique shotguns" every time I was asked.
-You and your RFD will be escorted to a police officer who will book the guns out of the UK. He does check paperwork and RFD.
-You have to wait while your package is inspected/xray.
-Once your baggage is accepted, you and the dealer are done. Enjoy the flight.
-I declared the antique guns on my duty card.
-I was flagged for hand inspection at US Customs. No surprise there.
-I explained the documentation and manifest
-I showed them the actions and barrels. They checked serial numbers against my Bill of Sale and documentation of age.
-It took less that 30 minutes once I got to a Customs Officer.

Good documentation is a must. Nigel Brown London/Birmingham books are accepted references. Proof marks and patent dates are a good backup if the makers production numbers are not published.
I had a nice little package of documentation that made it as easy as possible for customs to confirm pre-1898.

I picked an international flight to/from my hometown. I figured that if there were customs problems, I would not be stuck with having to go back and forth to Atlanta or Philly to resolve. Fortunately there were no issues.


Modern guns are another set of rules. The other postings pretty much cover those requirements. The economics of bringing back an antique work pretty well. The economics of modern guns are tough to justify except for the higher value guns. That's why you don't see a lot of sub $1500 English doubles in the US.

Joe in Charlotte