We present results from a multiwavelength study of the blazar PKS 1954–388 at radio, UV, X-ray, and gamma-ray energies. A RadioAstron observation at 1.66 GHz in June 2012 resulted in the detection of interferometric fringes on baselines of 6.2 Earth-diameters. This suggests a source frame brightness temperature of greater than 2 × 1012 K, well in excess of both equipartition and inverse Compton limits and implying the existence of Doppler boosting in the core. An 8.4-GHz TANAMI VLBI image, made less than a month after the RadioAstron observations, is consistent with a previously reported superluminal motion for a jet component. Flux density monitoring with the Australia Telescope Compact Array confirms previous evidence for long-term variability that increases with observing frequency. A search for more rapid variability revealed no evidence for significant day-scale flux density variation. The ATCA light-curve reveals a strong radio flare beginning in late 2013, which peaks higher, and earlier, at higher frequencies. Comparison with the Fermi gamma-ray light-curve indicates this followed ~ 9 months after the start of a prolonged gamma-ray high-state—a radio lag comparable to that seen in other blazars. The multiwavelength data are combined to derive a Spectral Energy Distribution, which is fitted by a one-zone synchrotron-self-Compton (SSC) model with the addition of external Compton (EC) emission.