Anti-resonant response of resonant inclusions?

When retrieving the material parameters of a metamaterial with resonant inclusions, the expected Lorentz-like resonance in one parameter typically yields an unexpected and unphysical so-called antiresonance in the other effective parameter. Using a simple model problem with plasmonic cylinders, we discuss some explanations for the antiresonance-problem and argue that the fundamental reason is that the assumed homogeneous model with sharp boundaries is insufficient when the retrieval fails to produce physically reasonable results. Some promising paths towards a better model are also briefly discussed.