  Supernova remnants (SNRs) are widely considered to be accelerators of cosmic
rays (CR). They are also expected to produce very-high-energy (VHE; $E > 100$
GeV) gamma rays through interactions of high-energy particles with the
surrounding medium and photon fields. They are, therefore, promising targets
for observations with ground-based imaging atmospheric Cherenkov telescopes
like the H.E.S.S. telescope array. VHE gamma-ray emission has already been
discovered from a number of SNRs, establishing them as a prominent source class
in the VHE domain. Of particular interest are the handful of SNRs whose X-ray
spectra are dominated by non-thermal synchrotron emission, such as the VHE
gamma-ray emitters RX J0852.0-4622 (Vela Jr.) and RX J1713-3946. The shell-type
SNRs G1.9+0.3 and G330.2+1.0 also belong to this subclass and are further
notable for their young ages ($\leq 1$ kyr), especially G1.9+0.3, which was
recently determined to be the youngest SNR in the Galaxy ($\sim100$ yr). These
unique characteristics motivated investigations with H.E.S.S. to search for VHE
gamma rays. The results of the H.E.S.S. observations and analyses are
presented, along with implications for potential particle acceleration
scenarios.
