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The evolution of high power microwave (HPM) sources into practical systems requires the development of compact pulsed power that can be integrated into mobile platforms. One approach to pursuing this objective, developed by researchers at Sandia National Laboratories (Sandia) [1], is to utilize parallel-stacked Blumlein transmission lines energized with a compact Marx generator. Such a configuration would be capable of driving low impedance HPM sources with a long pulse waveform. One of the limitations of this approach is field enhancement-induced breakdown at the edges of the line. Another limitation is percolation of, and subsequent breakdown of the liquid dielectric that is used in the system. This paper describes a research program that, both computationally and experimentally, is studying electrical breakdown in such transmission line configurations for a variety of dielectric materials and substrate geometries.