We investigate space-frequency block coding for OFDM systems with multiple transmit antennas, where coding is applied in the frequency domain (OFDM carriers) rather than in the time domain (OFDM symbols). In particular we consider Alamouti's code, which was shown to be the optimum block code for two transmit antennas and time domain coding. We show that the standard decoding algorithm results in significant performance degradation depending on the frequency-selective nature of the transmission channels, such that a low coherence bandwidth results in a huge degradation. The optimum decoding algorithm that alleviates this problem is the maximum-likelihood decoder for joint symbol detection. We present a performance analysis for the investigated space-frequency decoders in terms of the achievable BER results. Furthermore we compare space-time and spacefrequency coding and discuss the respective advantages and drawbacks of the different decoding algorithms in terms of their complexity. It should be noted that for the space-time approach we introduce the so-called matched-filter receiver, which shows significantly lower complexity compared to the maximum-likelihood decoder known from literature. The HIPERMAN system serves as an example OFDM system for quantitative comparisons.