The main characteristics in the radio continuum spectra of Supernova Remnants (SNRs) result from simple synchrotron emission. In addition, electron acceleration mechanisms can shape the spectra in specific ways, especially at high radio frequencies. These features are connected to the age and the peculiar conditions of the local interstellar medium interacting with the SNR. Whereas the bulk radio emission is expected at up to $20-50$ GHz, sensitive high-resolution images of SNRs above 10 GHz are lacking and are not easily achievable, especially in the confused regions of the Galactic Plane. In the framework of the early science observations with the Sardinia Radio Telescope in February-March 2016, we obtained high-resolution images of SNRs Tycho, W44 and IC443 that provided accurate integrated flux density measurements at 21.4 GHz: 8.8 $pm$ 0.9 Jy for Tycho, 25 $pm$ 3 Jy for W44 and 66 $pm$ 7 Jy for IC443. We coupled the SRT measurements with radio data available in the literature in order to characterise the integrated and spatially-resolved spectra of these SNRs, and to find significant frequency- and region-dependent spectral slope variations. For the first time, we provide direct evidence of a spectral break in the radio spectral energy distribution of W44 at an exponential cutoff frequency of 15 $pm$ 2 GHz. This result constrains the maximum energy of the accelerated electrons in the range $6-13$ GeV, in agreement with predictions indirectly derived from AGILE and textit{Fermi}-LAT gamma-ray observations. With regard to IC443, our results confirm the noticeable presence of a bump in the integrated spectrum around $20-70$ GHz that could result from a spinning dust emission mechanism.