We examine theoretically the Casimir effect between a metallic plate and several types of magnetic metamaterials in pursuit of Casimir repulsion, by employing a rigorous multiple-scattering theory for the Casimir effect. We first examine metamaterials in the form of two-dimensional lattices of inherently nonmagnetic spheres such as spheres made from materials possessing phonon-polariton and exciton-polariton resonances. Although such systems are magnetically active in infrared and optical regimes, the force between finite slabs of these materials and metallic slabs is plainly attractive since the effective electric permittivity is larger than the magnetic permeability for the studied spectrum. When lattices of magnetic spheres made from superparamagnetic composites are employed, we achieve not only Casimir repulsion but almost total suppression of the Casimir effect itself in the micrometer scale.