Metamaterials are artificial assemblies of multiple structures arranged in periodic patterns, designed to have electromagnetic properties that are not found in nature, such as negative refractive index, permittivity or permeability. Such properties enable a number of novel applications such as cloaking and can be utilized to reduce physical size or enhance operation of well-studied devices such as lenses, antennas and phase shifters. While applications of metamaterials were studied over the past decade, there are few reports on metamaterial structures capable of guiding and manipulating high-power microwaves. Generally, this is due to high losses generated in their structures, which is converted to heat. High-power applications exacerbate this problem by exposing the structure and the individual materials constituting it to high levels of columbic stress and thermal stress, exposing various nonlinearities in the electromagnetic properties of both the constituent materials and the overall structure. High-power environments are thus able to alter the operating characteristics of metamaterials. In extreme cases, runaway feedback loops might form, causing failure. This research has a two-prong approach. On one hand, nonlinearities appearing in high-power use cases are studied theoretically, to provide better simulations, especially concentrating on the prediction of catastrophic failure cases. In tandem, various matematerial structures are studied for a better understanding of their properties and limits as pertains to high-power applications.