Observations of supernova remnants (SNRs) are a powerful tool for investigating the later stages of stellar evolution, the properties of the ambient interstellar medium, and the physics of particle acceleration and shocks. For a fraction of SNRs, multi-wavelength coverage from radio to ultra high-energies has been provided, constraining their contributions to the production of Galactic cosmic rays. Although radio emission is the most common identifier of SNRs and a prime probe for refining models, high-resolution images at frequencies above 5 GHz are surprisingly lacking, even for bright and well-known SNRs such as IC443 and W44. In the frameworks of the Astronomical Validation and Early Science Program with the 64-m single-dish Sardinia Radio Telescope, we provided, for the first time, single-dish deep imaging at 7 GHz of the IC443 and W44 complexes coupled with spatially-resolved spectra in the 1.5-7 GHz frequency range. Our images were obtained through on-the-fly mapping techniques, providing antenna beam oversampling and resulting in accurate continuum flux density measurements. The integrated flux densities associated with IC443 are S_1.5GHz = 134 +/- 4 Jy and S_7GHz = 67 +/- 3 Jy. For W44, we measured total flux densities of S_1.5GHz = 214 +/- 6 Jy and S_7GHz = 94 +/- 4 Jy. Spectral index maps provide evidence of a wide physical parameter scatter among different SNR regions: a flat spectrum is observed from the brightest SNR regions at the shock, while steeper spectral indices (up to 0.7) are observed in fainter cooling regions, disentangling in this way different populations and spectra of radio/gamma-ray-emitting electrons in these SNRs.