We propose to use the effect of magnetosensitive microwave absorption (MMA) in a search for new superconducting materials. This effect is highly sensitive to superconducting phases in the sample, thus providing a means for detection of low concentrations of such phases (down to 10^-3 vol%). As non-superconducting materials also exhibit MMA, it is necessary to determine the characteristic features of the effect that are unique to the superconducting state. For this purpose, we have analysed MMA spectra of type I and type II superconductors, as well as of high-T_c superconductors, and compared these spectra with similar spectra taken for materials containing magnetic dipoles and for semiconductors exhibiting the effect of magnetoresistance. We determined the main characteristic features of MMA typical of the superconducting state and observed these in a number of oxide glasses doped with transition metals such as Cu, Ni, Co or Fe.