Fast-neutron/gamma-ray pulse-shape discrimination has been performed for the organic liquid scintillators NE 213A and EJ 305 using a time-of-flight based neutron-tagging technique and waveform digitization on an event-by-event basis. Gamma-ray sources and a Geant4-based simulation were used to calibrate the scintillation-light yield. The difference in pulse shape for the neutron and gamma-ray events was analysed by integrating selected portions of the digitized waveform to produce a figure-of-merit for neutron/gamma-ray separation. This figure-of-merit has been mapped as a function of detector threshold and also of neutron energy determined from time-of-flight. It shows clearly that the well-established pulse-shape discrimination capabilities of NE 213A are superior to those of EJ 305. The extra information provided by the neutron-tagging technique has resulted in a far more detailed assessment of the pulse-shape discrimination capabilities of these organic scintillators.