A metrological apparatus has a driver (33) that effects relative movement between a support (4) and a measurement probe (8) carriage (7) in a first direction (X) to cause the measurement probe (8) to traverse a measurement path along a surface of an object supported by the support. The measurement probe (8) moves in a second direction (Z) transverse to the first direction as it follows surface characteristics. Respective first and second position transducers (35, 32) provide first and second position data representing the position of the measurement probe in the first and second direction. A calibrator (300) carries out a calibration procedure using measurement data obtained on a surface of known form. The calibrator determines calibration coefficients of an expression relating corrected measurement data and the actual measurement data by using the known form of the reference surface as the corrected measurement data. The calibrator varies the calibration coefficient for Chebychev points until the at least one expression provides a fit to the data.