A non-zero neutron electric dipole moment (nEDM) would indicate time-reversal and charge-parity violation. Our collaboration is developing an experiment at TRIUMF to improve the sensitivity to the nEDM by one order of magnitude ($10^{-27}$~e$\cdot$cm). I developed a highly sensitive magnetometer based on nonlinear magneto-optical rotation (NMOR) in Rb vapour. In the future such magnetometers will serve in an array to form an auxiliary magnetometer system monitoring the stability and uniformity of the magnetic field in the nEDM experiment. The operation of the magnetometer in a free-induction-decay mode was the focus of this thesis. The precision of the field measurement, drifts over time, the impact of degaussing, and measurements of transverse fields were studied using the magnetometer.