Since seeing your post I was really interested in that name. I'd never seen it before, and really like it! So I've been looking around about it.
First I want to say that I did encounter the meaning "stone prince" in a few locations, and am not sure how much to believe that's correct. I'm not sure where they came up with that meaning because Arthmael seems to be a Welsh name, and "arth" means "bear," not "stone." I'm not sure what "stone" is in like ancient Celtic. I'd be curious since that's how "mael" comes by the meaning of "prince." I've also seen -mael on place names, so it could be some sort of suffix with a seperate meaning? Couldn't find anything out about that though.
Anyway, Kate should be right about the pronunciation. It should be ARTH-miel (miel sounds like the word mile). It might also be able to be pronounced -mayl, based on some other name I found. The th would be a soft one, as the one in "bath," not "the."
I also found that there was a Saint Arthmael (bonus awesomeness!)http://www.kingarthur.justwizard.com/Saint_Arthmael.html
And according to Wikipedia, Arthmael is the Welsh equivalent of Archmail, who was a King of the Britons. But who knows how true it being a form of the same name is.http://www.encyclo.co.uk/define/Archmail