There is a long history of, and renewed interest in, cardiac timing effects on behaviour and cognition. Cardiac timing effects may be identified by expressing events as a function of their location in the cardiac cycle, and applying circular (i.e. directional) statistics to test cardiac time-behaviour associations. Typically this approach ‘stretches’ all points in the cardiac cycle equally, but this is not necessarily physiologically valid. Moreover, many tests impose distributional assumptions that are not met by such data. We present a set of statistical techniques robust to this, instantiated within our new Cardiac Timing Toolbox (CaTT) for MATLAB: A physiologically-motivated method of wrapping behaviour to the cardiac cycle; and a set of non-parametric statistical tests that control for common confounds and distributional characteristics of these data. Using a reanalysis of previously published data, we guide readers through analyses using CaTT, aiding researchers in identifying physiologically plausible associations between heart-timing and cognition.