All you need for DMCA takedown notice is "a good faith belief" that reported content is infringing copyright you own (or is owned by someone you represent).
The opposing party has to prove that the claim was knowingly false and malicious for the claimant to be charged with perjury.
The opposing party has to prove actual damages in court to get any compensation. You may get legal fees back too (up to the court), but that's only likely to happen if it's obvious at the first glance that the claim was bogus.
This is all you can do to someone filing the notice. Notice doesn't even establish a jurisdiction (and cease-and-desist letter does) - so you can't counter-sue in your jurisdiction to get declaratory judgment that copyright is invalid.