Photocurrent correlation measurements used for the characterization of ultrafast photoconductive switches based on GaAs and silicon-on-sapphire are demonstrated. The correlation signal arises from the interplay of the photoexcited carriers, the dynamics of the bias field and a subsequent recharging of the switch. By using both photocurrent measurements and terahertz spectroscopy we verify the importance of space-charge effects on the carrier dynamics. Photocurrent nonlinearities and coherent effects are discussed as they appear in the correlation signals. An analysis based on a simple model allows an estimate of the carrier lifetimes associated with the photoconductive switching process. We illustrate how pulse propagation can be studied sequentially using this technique and how a minor modification of the experimental setup enables the study of screening from long-lived carriers. We emphasize in what ways the different techniques of measuring ultrashort electrical pulses are sensitive to different aspects of the pulse forming mechanisms.