The non-thermal nature of the X-ray emission from the shell-type supernova remnants (SNRs) G1.9+0.3 and G330.2+1.0 is an indication of intense particle acceleration in the shock fronts of both objects. This suggests that the SNRs are prime candidates for very-high-energy (VHE; E $>$ 0.1 TeV) {\gamma}-ray observations. G1.9+0.3, recently established as the youngest known SNR in the Galaxy, also offers a unique opportunity to study the earliest stages of SNR evolution in the VHE domain. The purpose of this work is to probe the level of VHE {\gamma}-ray emission from both SNRs and use this to constrain their physical properties. Observations were conducted with the H.E.S.S. (High Energy Stereoscopic System) Cherenkov telescope array over a mor...