Going abroad with a musket
In order to travel abroad with your musket you must have a Shot Gun Certificate and a European Firearms Pass (see here here for information on this). The musket must be in a shotgun bag with the gun’s number on the outside of the bag in large numerals.
It is probably possible to travel by air with a musket but these days it seems likely that it will involve a great deal of paperwork and general hassle so it’s probably best avoided.
It’s inevitable that different people will have different experiences and it’s likely that the process will vary from one port to another. The following is based on travel through Dover in 2013.
When passing through Customs you must tell the Customs officer on duty that you’re carrying a replica 17th century matchlock musket. It may help to offer your Shot Gun Certificate and your European Firearms Pass for inspection. It’s quite possible that the Customs officer will just wave you through. There’s a fairly slim chance that they’ll want to look at the musket. In 2013, the officer on the way out of Dover wanted to know what it was for, did it fire and where was it going to be used but this was purely out of interest in much the same way as anybody else would have asked. On the journey back to the UK, the officer asked somebody else in the office what he should do and then said to this unseen person ‘So you’re not interested then?’. That was it.