Supernova remnants (SNRs) are widely regarded as primary sources of galactic cosmic rays, owing to diffusive shock acceleration (DSA) operating at their forward shock fronts. Synchrotron radio emission from SNRs offers the most direct evidence for this mechanism. Here, we present a model for radio emission from evolved SNRs, assuming that radio-emitting electrons in the shells are accelerated via DSA in the test-particle approximation at the front of the main shock wave. The magnetic field required for synchrotron radiation is assumed to originate from the interstellar medium, compressed at the shock. This model successfully reproduces a broad range of observed radio properties of SNRs. SNR evolution generally encompasses free-expansion, Sedov-Taylor (adiabatic), and radiative phases, with the radiative phase presenting unique challenges for interpreting radio emission. We emphasize that the main shock wave, which envelops the entire SNR, serves as a persistent accelerator of cosmic rays from the supernova explosion until its sonic Mach number drops to $M \lesssim 2$. Notably, the self-sustaining character of DSA enables its operation even through the onset of the radiative phase, provided the surrounding interstellar medium is sufficiently uniform and ionized.