Two methods of improving non-invasive thermometry, by microwave radiometry, of the temperature in the body, are investigated. The temperature reading of an ordinary radiometer is a weighted average of the temperature distribution in the field of view of the antenna - the weighting decreasing with depth. The aim of both methods is to give a weighting with a maximum value at depth in the tissue. This is an improvement because the surface layers (skin and fat), having a thermo-regulatory role, may mask the sub-surface temperature. Various aspects of ordinary microwave radiometers are dealt with first. The antenna patterns were measured in liquid. tissue phantom using a small probe radiating wideband noise. Multi-frequency radiometry uses two radiometers operating at different frequencies, so with different weightings. Combining readings at 1 and 3 GHz gives a maximum at a depth of 1 cm, signal noise being increased by a factor of 2.5. The technique is limited to two frequencies because of the limited accuracy of the estimated weightings. Correlation radiometry employs two identical radiometers. The antennas are arranged to view a common region at depth in the tissue. The signal from this region alone is selected by cross-correlating the two signals. Two designs of correlation radiometer were constructed and tested. The pattern does have a maximum response at depth but it is also modulated by an interference pattern giving it a complicated form which will make interpretation of the output reading impossible or ambiguous. Close spacing of the antennas removes the interference pattern but it also removes the maximum at depth. The study was instigated to investigate the use of microwave radiometry for monitoring hyperthermia therapy. It will be of doubtful use in this application because of the limited penetration depth and poor resolution. In other clinical applications of microwave radiometry, multi-frequency radiometry will be a useful improvement.