The KCNH2 gene (known as hERG in humans) encodes the primary subunit of the rapid delayed rectifier potassium current IKr. IKr modulates cardiac action potential repolarisation and hERG expression affects action potential morphology. Consequently, the representation of hERG channel kinetics within mathematical action potential models has a great influence on simulations of cardiac electrical activity. This is true in control conditions but is also particularly evident when simulating the effects of drug block. Mathematical electrophysiology modelling forms a core part of a new proposal for routine preclinical cardiac safety assessment of pharmaceutical compounds (Sager et al., 2014). It is therefore important that hERG channel kinetics are accurately represented within mathematical models of cardiac electrophysiology to be used for such simulations. Many different mathematical models have been proposed to describe hERG channel kinetics. These models demonstrate a wide variety of behaviours when used to simulate both standard voltage-step and action potential protocols. We question whether all observed behaviours are expected experimentally; and if so, which model should we select to represent hERG within an action potential model in order to simulate cardiac electrical activity as accurately as possible? We have designed novel sinusoidal voltage protocols to rapidly explore hERG channel kinetics. Using a Bayesian inference approach we assessed the ability to use the protocols to parameterise hERG channel models. We recorded currents in response to these protocols in patch clamp experiments using hERG-transfected HEK-293 cells. The aim of this study was to determine the most appropriate model to describe hERG channel kinetics. We used experimental current recordings in response to the sinusoidal voltage protocols to parameterise a selection of candidate model structures. We then validated each model by assessing its ability to predict currents in response to traditional voltage-step protocols recorded from the same cell. We identify model structures which are both able to describe the experimental data to which they were fitted and additionally make representative predictions of the validation data. This provides some indication that the selected models encapsulate the kinetics of the ionic current, and are not simply a description of the data to which they were fitted. This study demonstrates the necessity of careful consideration of experimental design, model parameterisation and model selection when constructing mathematical ion channel kinetic models. Such considerations are likely to be important in determining more predictive mathematical models of cardiac electrophysiology.