Why would you go to the trouble and expense? You'll very likely get just as
good an answer, free and much more quickly, by showing a picture of your coin here on
Forvm!
A couple of years ago I sent an
aureus of
Septimius Severus to the BM, because it
had strangely been gilded, which made me worry a little about the authenticity, and the BM
had one from the same dies to compare it with. They approved it and sent it back to me in Chicago, but did ask me to reimburse their postal charges.
Again regarding authenticity, I once sent them 12 late
Roman bronzes that
had wrongly been condemned as modern
fakes by the
notorious moderator of a coin forgery discussion group. Two curators saw nothing wrong with the coins, found two die links to unquestionably genuine pieces that
had been in their own
collection for over a century, and sent them back to me in Chicago.
So there are no real problems with customs or shipping, apart from the slight risk that the coin will be stolen or otherwise lost underway.
But, to repeat, I certainly wouldn't recommend sending coins to the BM for IDs!