The TCV Tokamak was designed to create a large variety of plasma shapes. Such a large flexibility requires high precision magnetic measurements with a good spatial coverage. This article gives a detailed description of the magnetic sensor geometry, fabrication, calibration, the associated electronics, and the diagnostic operation and monitoring. A substantial effort has been made to quantify the precision in the measurements and a novel method has been developed to derive corrections in the sensor position and calibration which optimise the consistency of the entire measurement set. Accuracy of 0.5 mWb in the poloidal flux and 1 mT in the magnetic field with a position error of a few mm have been achieved. (C) 1998 American Institute of Physics. [S0034-6748(98)02006-1].