ABSTRACT Exomoons orbiting terrestrial or superterrestrial exoplanets have not yet been discovered; their possible existence and properties are therefore still an unresolved question. Here, we explore the collisional formation of exomoons through giant planetary impacts. We make use of smooth particle hydrodynamical collision simulations and survey a large phase space of terrestrial/superterrestrial planetary collisions. We characterize the properties of such collisions, finding one rare case in which an exomoon forms through a graze and capture scenario, in addition to a few graze and merge or hit and run scenarios. Typically however, our collisions form massive circumplanetary discs, for which we use follow-up N-body simulations in order to derive lower limit mass estimates for the ensuing exomoons. We investigate the mass, long-term tidal-stability, composition and origin of material in both the discs and the exomoons. Our giant impact models often generate relatively iron-rich moons that form beyond the synchronous radius of the planet, and would thus tidally evolve outward with stable orbits, rather than be destroyed. Our results suggest that it is extremely difficult to collisionally form currently-detectable exomoons orbiting superterrestrial planets, through single giant impacts. It might be possible to form massive, detectable exomoons through several mergers of smaller exomoons, formed by multiple impacts, however more studies are required in order to reach a conclusion. Given the current observational initiatives, the search should focus primarily on more massive planet categories. However, about a quarter of the exomoons predicted by our models are approximately Mercury-mass or more, and are much more likely to be detectable given a factor 2 improvement in the detection capability of future instruments, providing further motivation for their development.