I am not sure your question is very well posed, but to get any strong effect you need a strong wave-metamaterial coupling (eg for EM waves, some kind of electrical interaction, as per an appropriately designed metallic structure such as a split ring resonator or a fishnet). If you want a wide range of responses over a narrow bandwidth, then the structure itself will (also) have to have a similarly narrow resonance.

I suggest you first look at some of the basic literature on e.g. SRR's, or abstractions such as the Lorentz model, or the Drude model, to see how they behave and what they can do.