The soft demodulator is a key component of receivers that employ iterative demodulation and decoding. For multiple-input multiple-output systems with binary or QPSK signaling, the semidefinite relaxation (SDR) approach to list-based soft demodulation provides a desirable balance between the performance and computational cost. In this paper, that approach is extended to systems with higher order QAM signaling. For the class of list-SDR demodulators, the key to the extension is a quadratic approximation of the a priori information, and for the more computationally efficient class of single-SDR demodulators, the key to the extension is an algebraic expression, derived herein, for the probability that the SDR randomization procedure generates each candidate symbol. To implement these demodulators, customized primal-dual and dual-scaling algorithms are developed to solve the underlying semidefinite programs. The performance of the proposed demodulators is compared with that of some existing demodulators by using error-rate simulations, the empirical distribution of the computational cost, and EXIT chart analyses. In our comparisons, the proposed single-SDR demodulator provides performance that comes close to that of the list sequential demodulator at a computational cost that is close to that of the minimum mean-square error (parallel) soft interference canceller.