The possible use of microwave absorption at frequencies near the second harmonic of the electron cyclotron frequency for plasma diagnostics in tokamaks is investigated. Relations between the absorption characteristics and the plasma properties are derived and analyzed. The change in polarization as a wave propagates through an absorbing slab and outside it is determined. The analysis yields conditions under which absorption measurements can furnish information on the radial profile of the electron pressure, while polarization measurements yield information on the profile of the poloidal magnetic field in a tokamak.