It really depends on the country and the type of case. For BigLaw, see if a national firm has a presence in a foreign country.
For criminal cases, use the NACDL directory. The Big 4 are repeating history and practicing law again–remember Anderson Legal?
A foreign connection does not a foreign case make. If trial venue is in the US, a need to take evidence abroad does not convert your case into a foreign one.
Beware of foreign lawyers who think they know US procedure. If you haven’t been paid yourself, don’t even bother.
Expect a lot of irrelevant hocus pocus.
Never notarize a document in Hong Kong. Use 28 USC 1746 whenever possible; save yourself a trip to the Embassy and the thousands local Hong Kong lawyers will demand for no good reason.