  Strongly disordered pseudogapped superconductors are expected to display
arbitrary high values of kinetic inductance close to superconductor-insulator
transition (SIT) that makes them attractive for the implementation of
dissipationless superinductance. We develop the theory of the collective modes
in these superconductors and discuss associated dissipation at microwave
frequencies. We obtain the collective mode spectra dependence on the disorder
level and conclude that collective modes become relevant source of dissipation
and noise in the far vicinity of SIT.
