In electrokinetic trapping (EKT), the electroosmotic velocity of a buffer solution in one area of a microfluidic device opposes the electrophoretic velocity of the analyte in a second area, resulting in transport of DNA to a location where the electrophoretic and electroosmotic velocities are equal and opposite and DNA concentrates at charged nanochannels. The method does not require an optical plug localization, a considerable advantage as compared to preconcentration techniques previously presented. In the work reported here, the trapping process is preceded by a field-amplification in the sample reservoir to reduce trapping time, as field-amplified EKT is shown to be an effective technique to preconcentrate samples from larger volumes. A theoretical model explaining the principle of field-amplified EKT considers different ionic strengths and cross-sectional areas in the microchip segments. The model is supported by experimental data using nucleic acids and fluorescein as sample analytes. An incorporated poly(ethylene terephthalate) (PET) membrane provides anion exclusion due to a negatively charged surface. A fluidic counter flow supports the trapping process in 100 nm pores due to anion exclusion. An analysis of Joule heating gives evidence that temperature gradient focusing effects are negligible and charge exclusion is responsible for trapping. The theoretical model developed and experimentally demonstrated can be exploited for the preconcentration of cell free fetal DNA circulating in maternal plasma and other rare nucleic acid species present in large sample volumes.