The integrated radio spectrum of supernova remnants (SNRs) and the spatial variation of the spectral indices across these extended sources are powerful tools for studying the shocks and particle acceleration processes occurring in different SNR regions. Characterization of these processes requires sensitive flux density measurements and high-resolution images, which are not always available due to observing difficulties. We want to show the potentiality of the high-resolution SARAO MeerKAT legacy Galactic Plane Survey (SMGPS) images regarding the morphological and spectral characterization of 29 known galactic SNRs. We used the SMGPS data at $1.284$ GHz coupled with data from the GaLactic and Extragalactic All-sky Murchison Widefield Array (GLEAM) survey ($0.072-0.231$ GHz) to characterize the integrated spectrum of each source and search for spatial spectral variation through analysis of sensitive spectral index maps. We were able to redefine the exact morphology of four SNRs (G024.7-00.6, G051.4+00.7, G348.7+0.3, and G351.9+00.1), distinguishing them from unrelated sources or identifying new emission regions associated with them and never observed before. In many other cases, we identified in the SMGPS images several overlaid with the remnants, and we were able to estimate their spectral contribution through inspection of the spatial variation of the spectral indices across the remnants. The integrated spectral indices show a more uniform distribution with respect to what is obtained by considering the values reported in the literature. We show that new sensitive and high-resolution data are crucial to firmly constraining both the integrated and spatially resolved spectrum of SNRs, especially for the less studied objects of the southern hemisphere. The comparison of our SMGPS-GLEAM spectral index maps with IR, molecular, and gamma -ray images allowed us to investigate the nature of the peculiar remnant regions.