We report on microwave measurements on DyBa$_2$Cu$_3$O$_{7-rmdelta}$ monodomains grown by the top-seeded melt-textured technique. We measured the field increase of the surface resistance $R_{rm s}(H)$ in the a-b plane at 48.3 GHz. Measurements were performed at fixed temperatures in the range 70 K - $T_{rm c}$ with a static magnetic field $mu_0H<0.8$ T parallel to the c-axis. Low field steep increase of the dissipation, typical signature of the presence of weak links, is absent, thus indicating the single-domain behaviour of the sample under study. The magnetic field dependence of $R_{rm s}(H)$ is ascribed to the dissipation caused by vortex motion. The analysis of $X_{rm s}(H)$ points to a free-flow regime, thus allowing to obtain the vortex viscosity as a function of temperature. We compare the results with those obtained on RE-BCO systems. In particular, we consider strongly pinned films of YBa$_2$Cu$_3$O$_{7-rmdelta}$ with nanometric BaZrO$_3$ inclusions.