This paper addresses the problem of estimating linear time invariant models from observed frequency domain data. Here an emphasis is placed on deriving numerically robust and efficient methods that can reliably deal with high order models over wide bandwidths. This involves a novel application of the Expectation-Maximisation (EM) algorithm in order to find Maximum Likelihood estimates of state space structures. An empirical study using both simulated and real measurement data is presented to illustrate the efficacy of the EM-based method derived here.