Synchronous machines are commonly modelled using d- and g-axis equivalent circuits. Here, we present an approach to the ensuing parameter estimation problem which employs the technique of indirect inference. In indirect inference, an intermediary model is employed which is computed for both the true system and the preferred model, in this case the equivalent circuit model. We have used frequency response data from standard standstill machine tests as the intermediary model. The circuit parameters of the model are optimised, such that the measured difference between the standstill frequency responses of the equivalent circuit model and the true system are minimised.