I've mentioned the EM drive before and how it seems to violate Newton's third law. I hope it works because it would be a boon for space exploration. A recent Popular Mechanics article discusses it and summarizes its apparent incongruity with contemporary physics: "It's much more likely that the researchers are overlooking something than that much of our physics is wrong." Yes indeedy. That's called abductive reasoning or inference to the best explanation. The classic example is when astronomer's noticed that Uranus's orbit was not following the path Newton's laws dictated. The two explanations were that a) Newton's laws were wrong, or b) there's a gravity well somewhere out there pulling Uranus out of orbit. They calculated where the gravity well would be, pointed their telescopes there, and bingo! -- that's how Neptune was discovered.
Of course abduction is not absolute like deduction or even as strong as induction. Take three possible arrangements of three elements: X; Y; and XàY.
The first premise states the law XàY: if X is the case, then Y is the case. The second premise affirms that X is the case. Therefore Y is the case; in fact Y must be the case. All hail deduction! This is a pretty standard conditional syllogism, modus ponens in particular.
The first premise is that X is the case. The second is that Y is the case. We can take this to mean that whenever X is the case Y is also the case -- that is, whenever X is observed, Y is observed following it. So the conclusion is the law XàY. Of course, this could fail to be the case: induction is not deductively valid. If it were, we would call it deduction. As stated, this may commit the fallacy of post hoc ergo propter hoc (after this, therefore because of this). Perhaps X and Y occur together for something other than a strict causal relation flowing from X to Y. But the above formulation is just meant as an illustration.
The first premise states the law, if X is the case then Y is the case. The second premise affirms that Y is the case. From this we abductively infer that X is the case. This pretty clearly commits the deductive fallacy of affirming the consequent -- or would commit it if it were being presented as a deduction. It would also commit the inductive fallacy of post hoc ergo propter hoc -- if it were induction. The idea here is that we have a store of possible explanations for Y. We know the law, if X then Y. Therefore, one possible explanation of Y is X. Again, this is not deductively valid, but so what? We have several potential explanations for Y, X is available and is in fact the best explanation, so we abductively infer X.
Science constantly uses abductive reasoning; in fact, scientists were doing so for centuries before C.S. Peirce, a.k.a. the patron saint of philosophers of science, explained and validated it (this is one reason why you can't really study the philosophy of science without also studying the history of science). But it works enough of the time to justify its use. You can observe abductive reasoning in action by watching or reading any of the incarnations of Sherlock Holmes, despite the constant claims that he is using the science of deduction.
So, back to the EM drive. As with Uranus's orbit, the two possible explanations are that Newton's laws are wrong or we're missing something. The latter is much more likely, so absent further information, the best explanation is that Newton's third law is not being violated but that we are just not observing its application for some reason.
And this could be wrong. The example of Uranus's orbit is usually discussed alongside a similar problem with Mercury's. Newton's laws dictated that Mercury's orbit should follow a certain path and it wasn't. Easy! There's another gravity well between Mercury and the Sun that's pulling it out of its orbit. Except there wasn't. It turned out that the explanation here is that Newton's laws were wrong (or I would say, contra Thomas Kuhn, that Newton's laws needed to be supplemented for certain domains of measurement). We needed Einstein's theories of relativity to make sense of Mercury's orbit. Something like that could be the case with the EM drive, but again, it's probably not the best explanation. Yet.