In the framework of the Sardinia Radio Telescope (SRT) Early Science Program, we obtained single-dish high-resolution imaging of the Supernova Remnants IC443 and W44 at 7 GHz. By coupling them with SRT 1.5 GHz maps, we provided spatially-resolved spectral measurements that are highlighting a spread in spectral slope distribution. The observed features range from flat or slightly inverted spectra corresponding to bright radio limbs and filaments, to relatively steep spectra in fainter radio regions. Different theoretical possibilities explaining the above challenging findings are discussed. In particular, we exclude that the observed region-dependent wide spread in spectral slope distribution could be related to absorption processes. Our high-frequency results can be directly related to distinct electron populations in the SNRs including secondary hadronic electrons and resulting from different shocks conditions and/or undergoing different cooling processes. Integrated fluxes associated with the whole SNRs obtained by SRT in comparison with previous results in the literature support the evidence for a slight spectral steepening above 1 GHz for both sources, which could be related to primary electrons or more likely secondary hadronic electrons cut-offs.