There are several difficulties associated with the accurate measurement of low temperature in the presence of an intense magnetic field B. Most of the problems stem from the direct effect of the field on the thermometric properties of almost all of the commonly used sensors. Because the magnitude of the field effect, eg magnetoresistance, varies widely as a function of B, 7", and the thermometer itself, a careful selection process is necessary to minimize the error. As an aid to such a process, a detailed comparison is presented of the field-dependent errors, AT/T, as a function of 7-, of carbon, carbon-glass, germanium, and platinum resistance thermometers, thermistors, Si and GaAs diodes, thermocouples, capacitance thermometers, and several other less popular devices. Specific recommendations are made on the basis of the comparison. The related problem of magnetic field measurement is also examined, with emphasis on the recent characterizations of commercially available InAs, InSb, and GaAs Ha//effect probes. From the results of measurements over the 1.5-300 K range and to fields as high as 23 T, several encouraging conclusions may be drawn concerning the performance of the sensors as magnetometers in the 1% accuracy range.