Metamaterials are a growing area of interest in the electromagnetics community due to their highly uncommon wave-material interaction characteristics, and they can be modeled using transmission line (TL) based networks. From verification of negative refraction to modeling more complex devices such as invisibility cloaks and field rotators, TL metamaterials offer a tangible solution to modeling novel devices in 1-D, 2-D, and 3-D structures. While currently available TL metamaterials allow for a predictable and easily manufactured network, the need for periodic, regular grids make current TL metamaterials sub-optimal for devices with curved boundaries or realization on curved surfaces. Our work presents the theory and application of TL metamaterials on irregular, nonperiodic grids for modeling 2-D electromagnetic phenomena in TE polarization, allowing for accuracy in curved device boundary modeling and significantly increased adaptability in potential application to curved surfaces. Based on an irregular grid obtained using an unstructured surface mesher, irregularly-shaped individual cells are related to local medium parameters to represent an overall device. The design method is validated using simple scattering problems with known analytical solutions and simulation data through lumped-element circuit- network simulations. The design process is then applied to more complex devices such as the Luneburg lens and field rotator. Capabilities and limitations of this technique are tested and explored. A microstrip based version of this method is subsequently developed and investigated using circuit and full-wave simulation data as well as experiment of a printed-circuit realization.