The specification of design wave spectra is based on spectral parameters estimated from available wave data. Measured data allow high-resolution estimates to be made, but they suffer from sampling variability and often do not contain a sufficient number of measurements in extreme sea states. Hindcast data can be used to examine spectral features associated with extreme sea states, but they can be limited by resolution and are dependent on how the physics are incorporated in the source terms of the wave model. We examine and compare the effects of estimating JONSWAP spectrum peak enhancement factor from measured and hindcast data for a range of sea states but particularly those with large significant wave heights. In the case of measured data, we build on earlier work and review effects associated with different methods for processing measured time series data, including the effect of sampling frequency, record length, and smoothing. These are then contrasted with estimates made from typical hindcast data, including the effect of the spectral shape associated with different source terms - in particular the four-wave interaction term. Finally, we provide recommendations on how best to estimate the peak enhancement factor of the JONSWAP spectrum for design purposes.