ABSTRACT Computational models of the cardiac action potential are increasingly being used to investigate the effects of genetic mutations, predict pro-arrhythmic risk in drug development, and to guide clinical interventions. These safety-critical applications, and indeed our understanding of the cardiac action potential, depend on accurate characterisation of the underlying ionic currents. Four different methods can be found in the literature to fit ionic current models to single-cell measurements: (Method 1) fitting model equations directly to time constant, steady-state, and I-V summary curves; (Method 2) fitting by comparing simulated versions of these summary curves to their experimental counterparts; (Method 3) fitting to the current traces themselves from a range of protocols; and (Method 4) fitting to a single current trace from an information-rich voltage clamp protocol. We compare these methods using a set of experiments in which hERG1a current from single Chinese Hamster Ovary (CHO) cells was characterised using multiple fitting protocols and an independent validation protocol. We show that Methods 3 and 4 provide the best predictions on the independent validation set, and that the short information-rich protocols of Method 4 can replace much longer conventional protocols without loss of predictive ability. While data for Method 2 is most readily available from the literature, we find it performs poorly compared to Methods 3 and 4 both in accuracy of predictions and computational efficiency. Our results demonstrate how novel experimental and computational approaches can improve the quality of model predictions in safety-critical applications. Statement of Significance Mathematical models have been constructed to capture and share our understanding of the kinetics of ion channel currents for almost 70 years, and hundreds of models have been developed, using a variety of techniques. We compare how well four of the main methods fit data, how reliable and efficient the process of fitting is, and how predictive the resulting models are for physiological situations. The most widely-used traditional approaches based on current-voltage and time constant-voltage curves do not produce the most predictive models. Short, optimised experimental voltage clamp protocols can be used to create models that are as predictive as ones derived from traditional protocols, opening up possibilities for measuring ion channel kinetics faster, more accurately and in single cells. As these models often form part of larger multi-scale action potential and tissue electrophysiology models, improved ion channel kinetics models could influence the findings of thousands of simulation studies.