Following the recent successful synthesis and characterization of bulk SnTiO3, its energy landscape was studied by means of density functional theory, applying different exchange-correlation and hybrid functionals. Experimentally accessible structure candidates with composition ABX(3) were identified by a database search and global exploration approach. Besides the common octahedral coordination of Ti, also fourfold and fivefold coordination spheres emerged to be reasonable structural motifs. Among the predicted high-pressure modifications, the tetragonal perovskite structure turned out to be stable at pressures between 11 GPa and 15 GPa. The possibility of a paraelectric-to-ferroelectric phase transition of the tetragonal perovskite structure was investigated by modeling the phonon spectra and soft mode behavior. Despite substantial long wavelength transverse optical mode softening, the predicted high c/a-ratio in tetragonal perovskite SnTiO3 inhibits the formation of a spontaneous reversible polarization.