Dipole moments, which contribute to the intensities of rotational transitions and also affect reactivity, have been computed for nearly 80 compounds with up to 6 atoms containing silicon or phosphorus. More than a dozen of the set have been detected in interstellar or circumstellar media. The remaining ones are related to these, and several of them may be found in space in the future. We compare results from the commonly used B3LYP level of density functional theory with ab initio results at the coupled cluster CCSD(T)/RCCSD(T) levels of theory. Correlation consistent basis sets as large as quintuple ζ quality were used, and extrapolations to the estimated complete basis set (CBSE) limit were performed for almost all of the species with coupled cluster theory. In addition to evaluating the accuracy of the results against available data, we explore various issues: the critical importance of including diffuse basis functions, the range of basis set dependence exhibited by the suite of molecules, and the presence of low-lying excited states for some species. Dipole polarizabilities are also reported at the CCSD(T)/RCCSD(T) CBSE level.