I actually had this almost identical situation on Monday, so IMHO:
My approach is to find something (like an image, but ideally they have some content from your site too) on their website that is clearly YOURS (i.e. taken from your site), and reference the URL where it appears, and then you send a DMCA takedown notice directly to their webhost.
I wont get into all the details, but basically the DMCA has "safe harbor" provisions that allow the hosting company to avoid any responsibility for copyrighted material being on their servers as long as they follow the process when they get a DMCA complaint, which is basically they have to take down the offending page within 10 days and notify the hosting client that they got a DMCA. The hosting client then has X days to respond, at which time you have to provide proof of a lawsuit or it goes back live, etc
Google "DMCA" and "17 U.S.C 512" there is very specific language that must be in these notices, but the big hosting companies all have a process in place for these. Smaller ones sometimes try to play the "intermediary/referee" role, don't let them. If the hosting company wants to be safe, they will do it no questions asked. It's up to the other guy to decide whether to appeal.
You do have to be careful on this though, if there is no good faith copyright claim (i.e. not you just dont like what they said about you) then you can actually open yourself up to legal consequences. Typically only works with US based hosting companies too.
*disclaimer time, this should not be interpreted as legal advice nor the formation of a attorney/cleint relationship, consult an attorney for your specific legal case"