A comparison between realistic metamaterial (MTM) structures and theoretical, well-established dispersive material models, which predict the frequency dependence of the permittivity and the permeability, is performed in the present work. A number of highly subwavelength unit cells are analyzed that could potentially be used to achieve the epsilon-negative (ENG) parameters desired for the antenna applications studied in [1-4]. This presentation will give the effective permittivities and permeabilities of several simulated and measured ENG slabs and ENG cubical structures. For each of these classes of MTMs, it will be explained how the real and imaginary parts of the effective permittivities and permeabilities vary with frequency, how they are related to each other, and how low losses can be achieved. Several RF circuit-based and lumped element implementations to achieve the ε and μ values required for MTM-based efficient electrically small antenna systems have also been considered; those results will be shown in the presentation.