Is it correct using "even" and "still" together?

I've posted it in comments and gotten enough up votes to post it as answer.

Yes, it does sound slightly redundant. But, it is certainly common usage. And, definitely not incorrect.

I believe it adds emphasis.

Consider:

After a warning, he is still doing the same."

This guy got warned, and he is still doing it.

vs.

Even after a warning, he is still doing the same."

Despite being warned, he is still at it.

The meanings are extremely similar, but the second one adds a sense of exasperation to the statement. Perhaps exasperation is too strong of a word, but I cannot think of a better one. (I'm very open to suggestions for a better one!)

It is grammatically correct but I find it more refined to use continues instead of still.

For example,

Even after the warning, he is still cheating on the test.

vs.

Even after the warning, he continues to cheat on the test.

I find the second to be more appealing but it is all up to opinion.