[Pam Korda, Leigh Butler, Mike Edenfield]
When Elayne tries to use the Power on Mat in [LOC: 38, A Sudden Chill, 504], she describes the effect as "The flows just...vanished." It seems that the medallion works by dissolving or destroying Power flows. At Balticon 30 (April 1996), RJ said that the medallion only works on direct weavings of the Power (both saidin and saidar) against the wearer. Evidence that the medallion protects against saidin comes from [LOC: 44, The Color of Trust, 554]: Halima/Aran'gar channels at Mat and the medallion activates. Halima, being a male soul recycled into a woman's body, channels saidin.
Indirect effects of the Power, such as picking up a rock with Air and throwing it, or lightning (lightning was mentioned by RJ as a specific example), are not blocked. Thus, the failure of the medallion to protect against the lightning strike at the end of TFOH can be explained. Rand's belief that the medallion didn't protect Mat from a man's channeling was in error.
Given all that, there has been some debate over whether the medallion would protect Mat from the effects of the Seanchan Crystal Throne. The throne is supposed to be a ter'angreal that inspires awe and reverence in anyone who comes before it [Guide: 17, Seanchan, 160]. This raises some separate questions, such as exactly how a ter'angreal could "channel" without someone activating it, but the relevant thing to wonder is, is the power of the Throne a direct or indirect effect of the OP? If the former, that implies Mat's medallion would shield him from the Throne; if the latter, the medallion may not be able to protect him from it.
An interesting case to consider is the Mirror of Mists disguise that Lanfear was wearing as Keille in the Waste. Mat had his medallion on the whole time, yet he couldn't see through the disguise any more than anyone else. However, as Owen Pope points out, there is a difference in that the Crystal Throne seems to affect someone's thoughts directly, something like Compulsion, while the Mirror of Mists is probably just an alteration of the environment immediately around the person wearing the disguise (perhaps if Mat had tried to hug Keille, or something...)
So it seems that as long as the "awe" weaves have to touch Mat directly to mess with him, the medallion would protect him from the effects of the Crystal Throne. (Of course, since RJ has said that the action will never actually go to Seanchan, this may be a moot point, but it's interesting to consider.)