In this contribution, we present a novel closed-form bit error rate (BER) approximation for orthogonal space-time block codes employing rectangular quadrature amplitude modulation. The multiple-input multiple-output channel is assumed to be affected by arbitrarily spatially correlated Rayleigh fading. We consider a mismatched maximum-likelihood receiver that obtains the channel state information through pilot-based linear minimum mean-square error channel estimation. The presented BER approximation is shown to yield very accurate results over a wide range of signal-to-noise ratios.