A combination of space-time block coding and spatial modulation (STBC-SM) has been recently proposed for multiple input-multiple output systems to obtain both spatial diversity gain and more capacity simultaneously while assuming the perfect channel state information (P-CSI) was available at the receiver. However, in practical scenarios the CSI is unknown to the receiver and should be estimated in order to detect the transmitted data in a reliable way. Therefore, channel estimation (CE) is a major challenge in designing the STBC-SM systems. In this study, the problem of CE is investigated and a new pilot-aided channel estimation (PA-CE) technique, coupled with an interpolation, is proposed for the STBC-SM systems operating in the presence of rapidly time-varying mobile channels. Several interpolation schemes such as the linear, nearest neighbour, piecewise cubic Hermite and the low-pass interpolations are applied and their performances are compared to determine the best suitable interpolation technique to be employed in STBC-SM systems. Bit error rate (BER) performance of the proposed CE technique is then investigated in time-varying channels with different modulation. Moreover, the pairwise error probability of the STBC-SM scheme is derived and its average bit error probability is evaluated analytically in the presence of CE errors.