Understanding the roles of ion currents is crucial to predict the action of pharmaceuticals and also to guide clinical interventions in the heart, brain and other electrophysiological systems. Our ability to predict how ion currents contribute to cellular electrophysiology is in turn critically dependent on the characterization of ion channel kinetics. We present a method for rapidly exploring and characterizing ion channel kinetics, using the hERG channel, responsible for cardiac IKr current, as an example. We fit a mathematical model to currents evoked by a novel 8-second sinusoidal voltage clamp. The model is then used to predict over 5 minutes of recordings in the same cell in response to further voltage clamp protocols, including a new collection of physiological action potentials. Our technique allows rapid collection of data from single cells, produces more predictive ion current models than traditional approaches, and will be widely applicable to many ion currents.