The experimental and the theoretical interests for the silicon chemistry have been renewed by the recent detection of SiN in space. In this contribution a theoretical study of the HSiN, HNSi, HSiNH2 and HNSiH2 molecular systems is presented that aims to help in the interpretation of available experimental results as well as in the attribution of new interstellar lines. The main goal of this report remains, however, the calibration of ab initio calculations on still-unknown silicon-nitrogen systems: the infrared and the microwave signatures of the HSiNH+ cation are reported as a direct application. The signatures of the five molecules under investagation have been computed at increasing levels of post-Hartree-Fock theories, using up to a 6–311 + + G** atomic orbital expansion. Accurate geometries and Be rotational constants have been determined at the Möller-Plesset MPn(n = 2, 3, 4), CASSCF and CCSD(T) theoretical plateaus for HNSi. The comparison with experimental data allows then to derive the scaling factors needed to obtain accurate rotational constants for related species: they are applied as such on the crude constants determined for HSiN, HSiNH2, HNSiH2, and finally HSiNH2 in its floppy linear singlet ground state and in its lowest cis-bent a3A' state as well. Dipole moments are reported in order to assess the feasability for these species to be detected owing to their rotational signatures either in the laboratory or in space using millimetric radioastronomy techniques. Infrared (IR) signatures are computed at the same levels of theory and compared to the recent matrix isolation experiments devoted to HSiN, HNSi, HSiNH2 and HNSiH2. The calculations unambiguosly confirm that all these species have been effectively produced and observed. They also lead to the determination of accurate IR scaling factors that are significantly larger than the usual ones. Such an approach allows then to quantitatively predict the IR spectra of the still-unknown HSiNH+ entity. The study of the IR spectra furthermore points out the failure of single-reference correlation methods to obtain predictive IR signatures in some cases, as is unambigously illustrated in the case of the HSiN species.