Sensing coils are inductive sensors commonly used to measure magnetic fields, such as those generated by electromagnets used in many kinds of industrial and scientific applications. Inductive sensors rely on integrating the output voltage at the coil's terminals in order to obtain flux linkage, which may suffer from the magnification of low-frequency noise resulting in a drifting integrated signal. This article presents a method for the cancellation of integrator drift. The method is based on a first-order linear Kalman filter combining the data from the coil and a second sensor. Two case studies are presented. In the first one, the second sensor is a Hall probe, which senses the magnetic field directly. In a second case study, the magnet's excitation current was used instead to provide a first-order approximation of the field. Experimental tests show that both approaches can reduce the measured field drift by three orders of magnitude. The Hall probe option guarantees, in addition, one order of magnitude better absolute accuracy than by using the excitation current.