Here we discuss the limits to temporal resolution in nanopore sensor recordings, which arise from considerations of both small-signal frequency response and accumulated noise power. Nanopore sensors have strong similarities to patch-clamp ion channel recordings, except that the magnitudes of many physical parameters are substantially different. We will present examples from our recent work developing high-speed nanopore sensing platforms, in which we physically integrated nanopores with custom low-noise complementary metal-oxide-semiconductor (CMOS) circuitry. Close physical proximity of the sensor and amplifier electronics can reduce parasitic capacitances, improving both the signal-to-noise ratio and the effective temporal resolution of the recordings.