  We investigate the physics of the microwave response in
YBa$_{2}$Cu$_{3}$O$_{7-\delta}$, SmBa$_{2}$Cu$_{3}$O$_{7-\delta}$ and MgB$_{2}$
in the vortex state. We first recall the theoretical basics of vortex-state
microwave response in the London limit. We then present a wide set of
measurements of the field, temperature, and frequency dependences of the vortex
state microwave complex resistivity in superconducting thin films, measured by
a resonant cavity and by swept-frequency Corbino disk. The combination of these
techniques allows for a comprehensive description of the microwave response in
the vortex state in these innovative superconductors. In all materials
investigated we show that flux motion alone cannot take into account all the
observed experimental features, neither in the frequency nor in the field
dependence. The discrepancy can be resolved by considering the (usually
neglected) contribution of quasiparticles to the response in the vortex state.
The peculiar, albeit different, physics of the superconducting materials here
considered, namely two-band superconductivity in MgB$_{2}$ and superconducting
gap with lines of nodes in cuprates, give rise to a substantially increased
contribution of quasiparticles to the field-dependent microwave response. With
careful combined analysis of the data it is possible to extract or infer many
interesting quantities related to the vortex state, such as the
temperature-dependent characteristic vortex frequency and vortex viscosity, the
field dependence of the quasiparticle density, the temperature dependence of
the $\sigma$-band superfluid density in MgB$_{2}$
