Although radio emission is the most common identifier of Supernova Remnants (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. Located on the Sardinia island (Italy), the 64-m Sardinia Radio Telescope (SRT) is designed to observe in the 0.3-115 GHz frequency range. We performed single-dish imaging of the well-known SNRs such as IC443 and W44 at 3.5, 7.2 and 21.4 GHz with 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, which are not easily achievable through interferometry at these frequencies due to the very large SNR structures. SRT continuum maps of our targets are comparable with VLA maps carried out at lower frequencies (at 324 MHz and 1.4 GHz), providing a detailed structure of their complex filamentary morphology. New estimates of the total flux density are given in addition to flux measurements in different regions of the SNRs.