This paper studies the performance of antenna selection (AS) for space-time (ST) coded systems with noisy channel estimates. For coherent AS systems operating over Rayleigh flat fading channels, we derive the pairwise error probability (PEP) in the presence of imperfect channel estimation, where the channel is estimated using training insertion and MMSE estimation. Multiplexed training is employed, where the antennas are multiplexed to the small number of RF chains available in the AS system. AS is performed only at the receiver, using the maximum estimated channel power selection rule. Both the ML decoder taking into account the channel estimation error, and the minimum distance decoder are considered, and full spatial diversity is shown to be preserved for both cases. Based on the derived training-based PEP, the effective SNR and the coding gain loss due to training are quantified for square unitary and orthogonal codes. The optimal power allocation between the training and data symbols is obtained by minimizing the PEP. Closed-form exact PEP expressions are derived for AS systems employing orthogonal designs. When square unitary training is employed, we further propose an alternate training scheme which avoids multiplexing, has higher spectral efficiency, and better performance compared to the multiplexed training scheme.