We present single-dish imaging of the well-known Supernova Remnants (SNRs) IC443 and W44 at 1.5 GHz and 7 GHz with the recently commissioned 64-m diameter Sardinia Radio Telescope (SRT). Our images were obtained through on-the-fly mapping techniques, providing antenna beam oversampling, automatic baseline subtraction and radio-frequency interference removal. It results in high-quality maps of the SNRs at 7 GHz, which are usually lacking and not easily achievable through interferometry at this frequency due to the very large SNR structures. SRT continuum maps of our targets are consistent with VLA maps carried out at lower frequencies (at 324 MHz and 1.4 GHz), providing a view of the complex filamentary morphology. New estimates of the total flux density are given within 3% and 5% error at 1.5 GHz and 7 GHz respectively, in addition to flux measurements in different regions of the SNRs.