In this paper, the problem of joint channel and carrier frequency offset (CFO) estimation is studied in the context of multiple-input multiple-output (MIMO) communications based on orthogonal space-time-block codes (OSTBCs). A new blind approach is proposed to jointly estimate the channel matrix and the CFO parameters using a relaxed maximum likelihood (ML) estimator that, for the sake of simplicity, ignores the finite alphabet constraint. Although the proposed technique can be applied to the majority of OSTBCs, there are, however, a few codes that suffer from an intrinsic ambiguity in the joint channel, CFO, and symbol estimates. For such specific OSTBCs, a semiblind modification of the proposed approach is developed that resolves the aforementioned estimation ambiguity. Our simulation results demonstrate that although the finite alphabet constraint is relaxed, the performance of the proposed techniques approaches that of the informed (fully frequency-synchronized and coherent) receiver, provided that a sufficient number of data blocks is available for each channel realization.