How, if at all, can a memristor be emulated with active components?
The answer is: Mutator. Or maybe: M-R mutator.

The gyrator, used to emulate some properties of an inductor using a capacitor, is a subset of a mutator. I am not aware of a specific name for the type of mutator that gives you a memristic behavior (other than M-R mutator), but it seems like you can actually build it with real, existing components:



Source: Memristor - The Missing Circuit Element, Leon O. Chua, IEEE Transactions on Circuit Theory, Vol. CT-18, No. 5, September 1971.

The paper also shows how you can build a curve tracer for a memristor, i.e. a device that shows you a diagram for charge vs. flux-linkage. While there's a lot of theory in the paper, I like it because there are actual circuits I am sure one can breadboard and hack around with.