The electromagnetic properties of vacuous curved spacetime and of a certain fictitious material in flat spacetime are noncovariantly equivalent. This fictitious medium-known as the Tamm medium-is generally bianisotropic and nonhomogeneous. The Tamm medium offers opportunities for exploring the electromagnetic properties of certain curved-spacetime scenarios that may be impractical to explore by direct methods. The realization of various Tamm mediums as homogenized composite mediums was investigated. The approach taken involved the homogenization of relatively simple component materials, with the inverse Bruggeman formalism exploited to estimate appropriate constitutive parameters, shape parameters, and volume fractions for the component materials. Typically, Tamm mediums are highly anisotropic in regions corresponding to relatively large spacetime curvature (e.g., in the vicinity of spacetime singularities). In principle, at least, such high degrees of anisotropy may be achieved by homogenizing component particles that are highly elongated. The nonhomogeneous nature of Tamm mediums can be accommodated by adopting a piecewise homogeneous approach, which is valid for appropriate wavelength regimes.