The combination of Space-Time Coded Multiple Input Multiple Output systems (STC-MIMO) with Orthogonal Frequency Division Multiplexing (OFDM) is recently being investigated as an effective means of providing high-speed data transmission over dispersive wireless channels. The strengths of the two techniques coalesce and render MIMO-OFDM systems robust to ISI and IBI. However, the decoding and demodulation of STC-OFDM needs reliable channel knowledge at the receiver, unless differential modulation techniques are used. Semi-blind methods for channel estimation are seen to provide the best trade-off in terms of bandwidth overhead, computational complexity and latency. The conventional Expectation-Maximization (EM) algorithm for semi-blind channel estimation improves a pilot-based estimate with a two step process; however, it is computationally complex to implement. In this paper, we propose a variant of the EM method, referred to as ML-EM, for semi-blind estimation of doubly dispersive channels in space-time coded MIMO-OFDM systems. Here, the conventional EM algorithm is coupled with the ML decoder for space time block codes (STBCs). The technique shows good performance, even in highly correlated antenna arrays, and is computationally simpler than conventional EM. The method incurs a training overhead of less than 1%, and performs close to exact CSI through iterative processing at the receiver.