We present an experimental and computational study of the response of twisted-cross metamaterials that provide near dispersionless optical rotation across a broad band of frequencies from 19 GHz to 37 GHz. We compare two distinct geometries: firstly, a bilayer structure comprised of arrays of metallic crosses where the crosses in the second layer are twisted about the layer normal; and secondly where the second layer is replaced by the complementary to the original, i.e. an array of cross-shaped holes. Through numerical modelling we determine the origin of rotatory effects in these two structures. In both, pure optical rotation occurs in a frequency band between two transmission minima, where alignment of electric and magnetic dipole moments occurs. In the cross/cross metamaterial, the transmission minima occur at the symmetric and antisymmetric resonances of the coupled crosses. By contrast, in the cross/complementary-cross structure the transmission minima are associated with the dipole and quadrupole modes of the cross, the frequencies of which appear intrinsic to the cross layer alone. Hence the bandwidth of optical rotation is found to be relatively independent of layer separation.