For the EmDrive it also was that the claimed theoretical mechanism was mathematically impossible, because it was based on equations that (like all known equations and everything ever observed) satisfy the conservation laws.
That's a good question actually. Supposedly this is extracting energy from the rotational kinetic energy of the earth. I haven't looked at the paper but you'd need to worry about conservation of angular momentum here.
Given that the cited physicists didn't dismiss this out of hand I assume this is accounted for somewhere...