  We extend our previous work [Phys. Rev. Lett. {\bf 100}, 183602 (2008)] on
the generalization of the Casimir-Lifshitz theory to treat anisotropic
magnetodielectric media, focusing on the forces between metals and
magnetodielectric metamaterials and on the possibility of inferring magnetic
effects by measurements of these forces. We present results for metamaterials
including structures with uniaxial and biaxial magnetodielectric anisotropies,
as well as for structures with isolated metallic or dielectric properties that
we describe in terms of filling factors and a Maxwell Garnett approximation.
The elimination or reduction of Casimir "stiction" by appropriate engineering
of metallic-based metamaterials, or the indirect detection of magnetic
contributions, appear from the examples considered to be very challenging, as
small background Drude contributions to the permittivity act to enhance
attraction over repulsion, as does magnetic dissipation. In dielectric-based
metamaterials the magnetic properties of polaritonic crystals, for instance,
appear to be too weak for repulsion to overcome attraction. We also discuss
Casimir-Polder experiments, that might provide another possibility for the
detection of magnetic effects.
