A method for the precise measurement of drift times for the high-precision drift chambers used in the TWIST detector is described. It is based on the iterative correction of the space-time relationships by the time residuals of the track fit, resulting in a measurement of the effective drift times. The corrected drift-time maps are parametrised individually for each chamber using spline functions. Biases introduced by the reconstruction itself are taken into account as well, making it necessary to apply the procedure to both data and simulation. The described calibration is shown to improve the reconstruction performance and to extend significantly the physics reach of the experiment.