We systematically investigated the influence of polymer coating on temporal resolution of solid-state nanopores. We fabricated a Si3N4 nanopore integrated with a polyimide sheet partially covering the substrate surface. Upon detecting the nanoparticles dispersed in an electrolyte buffer by ionic current measurements, we observed a larger resistive pulse height along with a faster current decay at the tails under larger coverage of the polymeric layer, thereby suggesting a prominent role of the water-touching Si3N4 thin film as a significant capacitor serving to retard the ionic current response to the ion blockade by fast translocation of particles through the nanopores. From this, we came up with back-side polymer-coated chip designs and demonstrated improved pore sensor temporal resolution by developing a nanopore with a thick polymethyl-methacrylate layer laminated on the bottom surface. The present findings may be useful in developing integrated solid-state nanopore sensors with embedded nanochannels and nanoelectrodes.