Extrapolation of the dielectric response (particularly losses) from far infrared (IR) to microwave (MW) range is discussed, and it is shown that in the case of quasi-harmonic materials it yields the upper estimate of intrinsic (multi-phonon) microwave losses. The prediction is verified on many well-processed microwave ceramics of commercial as well as laboratory origin by using various submillimetre (SMM) transmission techniques. The advantage of the transmission techniques compared to less sensitive reflectivity measurements is emphasised. Steep increase in losses with increasing permittivity is accompanied by an increase in lattice anharmonicity, and finally (for very high permittivity) by the appearance of additional relaxations below the polar phonon frequencies. The temperature dependences of dielectric losses are reviewed and discussed. (C) 2002 Elsevier Science B.V. All rights reserved.