The Emdrive is an experiment that has so far provided an anomalous result. If that result holds up to replication and deeper investigation, only then will we proceed to the theory stage.

There is presently no theory to explain this result, but there are many speculations and hypotheses. Only the most extreme of these invoke a true violation of conservation laws, and these as a result would be considered last after others had been ruled out.

Less extreme hypotheses include interaction with dark matter or some other normally invisible or weakly interacting medium, unknown physics surrounding gravity or magnetic fields, etc.

Personally my favorite is dark matter. Could this be a weakly interacting particle thruster? Perhaps it is somehow accelerating ubiquitous but weakly interacting particles, essentially using dark matter as a propulsive medium.

That could have massive practical implications and would also lead to new physics, but would not violate conservation laws since momentum is being transferred.

A craft powered by such a thruster would have a "jet wash," just one that is harmless and largely undetectable through normal means. It might also only work in the vicinity of massive objects or in other places where a sufficiently rich concentration of propellant is found. Planets and stars have been hypothesized as being surrounded by dark matter clouds, but e.g. it may not work well in interstellar space.

Of course it would only be useful for propulsion if it could be made efficient.