Recent developments in metamaterials, or nanostructured materials with engineered optical properties, enable the creation of previously impossible devices. Optical cloaks, superlenses, optical black holes, and more are now theoretically possible, but robust methods to characterize the linear and nonlinear optical properties of these materials are critical to the evaluation and development of devices. First, this work is concerned with the linear optical characterization of general sub-wavelength periodic metal-dielectric nanostructures - optical metamagnetics - capable of producing magnetic responses in the visible. Then, nonlinear characterization of a nanoantenna type metamaterial is examined in the context of the optimal design of a thin-film optical limiting device. Optical limiting, or the ability to maintain high low intensity transmission and yet significantly attenuate or ‘limit’ high intensity throughput, has a wide variety of applications, most significantly for sensor protection or protective eyeware. In this work, the high local fields present in plasmonically resonant metamaterials are used to enhance the nonlinear response of a dye, resulting in a higher nonlinear absorption relative to the incident intensity, and a significant increase in the ‘effective’ nonlinear absorption coefficient. This work provides a foundation of linear and nonlinear characterization tools applicable to all metamaterials, but which is focused on optical limiting optimization.