In this article, we analyze the dispersion features of cloaking structures formed by plasmonic materials and/or metamaterials. Following our recent proposal for realizing a cloaking metamaterial shell capable of drastically suppressing the total scattering of moderately-sized objects, we investigate the frequency response and dispersion behavior of this anomalous phenomenon. Insights into the scattering reduction and possibility of multi-frequency response are presented, considering the inherent dispersion constraints of passive materials.