We have developed a numerical framework that allows estimation of coherence in spatiotemporal and spatiospectral domains. Correlation properties of supercontinuum (SC) pulses generated in a bulk medium are investigated by means of second-order coherence theory of non-stationary fields. The analysis is based on simulations of individual space–time and space–frequency realizations of pulses emerging from a 5 mm thick sapphire plate, in the regimes of normal, zero, and anomalous group velocity dispersion. The temporal and spectral coherence properties are analyzed in the near field (as a function of spatial position at the exit plane of the nonlinear medium) and as a function of propagation direction (spatial frequency) in the far field. Unlike in fiber-generated SC, the bulk case features spectacularly high degrees of temporal and spectral coherence in both the spatial and spatial-frequency domains, with increasing degrees of coherence at higher pump energies. When operating near the SC generation threshold, the overall degrees of temporal and spectral coherence exhibit an axial dip in the spatial domain, whereas in the far field, the degree of coherence is highest around the optical axis.