Fundamental understanding of carrier mobility related prebreakdown phenomena in dielectrics provides insights into high field transport phenomena as well as associated aging and onset of charge injection induced instability. A system for measuring resistive current through a dielectric film during a ramp voltage to breakdown has been developed to address the limits of conventional steady-state approaches in which the sample typically fails prior to achieving steady state current at around sixty percent of breakdown field. Prebreakdown conduction in polypropylene, polystyrene, and polyethylene-terephthalate thin films with varying molecular structure, crystallinity, and chain orientation were studied under room temperature as well as elevated temperature. Space-charge-limited current spectroscopy is used in the data analysis to extract more information from the experimental data. Critical transport parameters, such as prebreakdown density of bulk trap states, were extracted to provide a quantitative basis for comparative study and material engineering for improved high field performance.