At the ANS seminar Counterfeits: the Threat to Collecting and Scholarship several people from the museum community remarked analyzing the metal in coins using X-ray fluorescence (XRF). This technique is said by some people to be nearly as good as other techniques that are much more expensive.
If a coin contains modern elements, or if a coin has a different composition than a large group of known genuine coins, then it is likely false.
I asked who can provide such a service to private collectors — but no one had recommendations.
I received an unsolicited email recently from Phil Keck at Artemis Testing Lab. They offer XRF on ancient materials for $200. Two samples per item.
An eBay search found a service in Flushing Queens that will test coins (or anything else) for $20 a sample. The auction picture shows a Niton XL2 gun. Such guns can be purchased for $15-20k. I believe they can be rented as well. I am not sure how common such services are. A friend told me several years ago of one in a coin shop in Louisville KY.
If anyone has submitted ancient coins for XRF testing I would be curious to see what kind of reports you received and if they were helpful. If anyone is near New York and wants to try the service in Flushing or knows of a similar one perhaps a field trip could be organized to test coins. Any takers?