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 more than six-year period spanning 2004–2010 . The obtained data have effective livetimes of 67 h for G1.9 + 0.3 and 16 h for G330.2 + 1.0 . The data are analyzed in the context of the multi-wavelength observations currently available and in the framework of both leptonic and hadronic particle acceleration scenarios . No significant \gamma -ray signal from G1.9 + 0.3 or G330.2 + 1.0 was detected . Upper limits ( 99 % confidence level ) to the TeV flux from G1.9 + 0.3 and G330.2 + 1.0 for the assumed spectral index \Gamma = 2.5 were set at 5.6 \times 10 ^ { -13 } cm ^ { -2 } s ^ { -1 } above 0.26 TeV and 3.2 \times 10 ^ { -12 } cm ^ { -2 } s ^ { -1 } above 0.38 TeV , respectively . In a one-zone leptonic scenario , these upper limits imply lower limits on the interior magnetic field to B _ { G 1.9 } \gtrsim 11 \mu G for G1.9 + 0.3 and to B _ { G 330 } \gtrsim 8 \mu G for G330.2 + 1.0 . In a hadronic scenario , the low ambient densities and the large distances to the SNRs result in very low predicted fluxes , for which the H.E.S.S . upper limits are not constraining .