Increasing the throughput and resolution of electrical recording of currents through ion conducting channels and pores is an important technical challenge both for the functional analysis of ion channel proteins and for the application of nanoscale pores in single molecule analytical tasks. We present a novel design based on sub-picoliter-cavities arrayed in a polymer substrate and endowed with individual planar microelectrodes that allows low-noise and parallel electrical recording from ion channels and pores. Resolution of voltage-dependent current transitions of alamethicin channels as well as polyethylene-glycol-induced blocking events of alpha-hemolysin nanopores on the submillisecond time scale is demonstrated using this device.