The measurement of the transient pulsed electromagnetic (EM) field is essential for analyzing electromagnetic compatibility. Due to their good performance, D-dot sensors, combined with numerical integration computation for signal recovery, are commonly used to measure electromagnetic pulses (EMPs). However, the integration approach is occasionally flawed due to a non-ideal frequency response or noise, causing distortions in the reconstructed signal. In order to better understand the dynamic performance of the sensor, a nonlinear Hammerstein model is employed in the system identification for the sensor with the calibration data collected in the laboratory environment. When identifying the linear component based on the ultra-wideband characteristics of the measured transient pulse, a two-step identification approach with two different pulse excitation modes, low frequency and high frequency, is utilized to conduct the modeling across the entire frequency range. Based on the reliable identification and modeling of the D-dot sensor, a compensation system that corresponds to the nonlinear Hammerstein model has been developed for the practical signal recovery of the incident E-field. After compensation, the dynamic characteristics of the sensor are significantly improved, and the system compensation approach outperforms the integration method in signal recovery for the incident E-field.