In the analysis of the steady-state performances of saturated synchronous machines using the classical two-axis (d- and q-axis) frame model, the accurate calculation of the machine performances depends to a large extent on their saturation conditions. However, the effect of saturation depends not only on the saturation level in the axis of the resultant machine ampere-turns (intermediate-axis) but also on the phase angle between the resultant ampere-turns and the resultant magnetic flux. This paper presents four analytical methods for determining the intermediate-axis saturation characteristics of salient-pole synchronous machines from the measured d-axis saturation characteristics. The accuracies of these four methods have been verified by comparing the measured field currents and load angles of two laboratory salient-pole synchronous machines of different designs with those calculated using an innovated approach which uses the intermediate-axis saturation, characteristics directly in the modeling of the saturated synchronous machines. Moreover, the calculated intermediate-axis saturation characteristics have been compared with the measurable ones in the case of one of these machines.