Reciprocal licencing for amateur radio is fairly straightforward in the free world. The UK full amateur licence carries 'CEPT privileges' - so you can operate amateur radio equipment when holidaying in the EU and some nearby countries like Turkey that have signed up to it.
I found this very useful on my Arctic Circle trip, and got useful advice from local Finnish hams with my dual band handheld.
The American FCC have an agreement with the CEPT countries. If you have a US licence , you can operate in CEPT countries very easily. You just need your ham licence, passport and a printout of the relevant FCC notice. In fact I have often worked Americans holidaying in the UK.
Similarly, my UK licence allows me to operate in the US and Canada. I am, however, bound to the UK power restrictions (400 watts, as opposed to the 1.5 kW that an American ham can use at home.)
Thanks. I assume if an American ham operating in Britain would be subject to the lower UK power restrictions rather than the higher ones he was licensed for at home? Likewise for allowed frequencies? In other words; If the home nation rules and the host nation rules differ then obey the most restrictive?