This paper presents recent advances in the development of HEMP waveforms with causal responses suitable for implementation in Finite Difference Time Domain models. New time-domain implementations of the HEMP environment are proposed using direct and indirect employment of the HEMP waveform. Numerical instabilities of the waveform are addressed and a new stable waveform matched to the IEC standard has been evaluated. It is concluded that the implementation of the quotient exponential model provides a stable and accurate waveform for time-domain modelling.