We report on the fabrication, simulation, and characterization of insulated nanoelectrodes aligned with nanopores in low-capacitance silicon nitride membrane chips. We are exploring these devices for the transverse sensing of DNA molecules as they are electrophoretically driven through the nanopore in a linear fashion. While we are currently working with relatively large nanopores (612 nm in diameter) to demonstrate the transverse detection of DNA, our ultimate goal is to reduce the size sufficiently to resolve individual nucleotide bases, thus sequencing DNA as it passes through the pore. We present simulations and experiments that study the impact of insulating these electrodes, which is important to localize the sensing region. We test whether the presence of nanoelectrodes or insulation affects the stability of the ionic current flowing through the nanopore, or the characteristics of DNA translocation. Finally, we summarize the common device failures and challenges encountered during fabrication and experiments, explore the causes of these failures, and make suggestions on how to overcome them in the future.