Gamma-ray bursts (GRBs) and supernovae (SNe) are well known examples of celestial transient events. Their tremendous energy release provides the ability to accelerate particles to the highest energies. The High Energy Stereoscopic System (H.E.S.S.) is an array of four imaging atmospheric Cherenkov telescopes, covering gamma-ray energies between 100 GeV and 100 TeV (VHE range). In this work the H.E.S.S. data on GRBs are searched for VHE gamma-ray emission. Amongst them is the analysis of GRB 100621A, the brightest X-ray source so far detected by the Swift satellite. Measurements at lower energies make it a promising candidate within the sensitivity reach of the H.E.S.S. instrument, however no indication of VHE emission is found. The derived upper limits constrain the existence of additional spectral components and provide important input for understanding the emission process. Furthermore, H.E.S.S. pointing positions are compared to a recently created, unified SN catalogue in order to identify extragalactic SNe accidentally in the field of view during the observation of other targets. The analysis reveals no significant detection, which allows one to constrain possible VHE emission scenarios. This work also includes a technical discussion of the H.E.S.S. telescope pointing accuracy. A new approach, the SingleCCD concept, is discussed and evaluated, which is interesting for the next generation of imaging atmospheric Cherenkov telescopes
