A method of calibrating a coordinate positioning machine having a first member that is moveable relative to a second member, wherein the geometry of the machine is characterised by a set of model parameters. The machine is controlled to make point contact between multiple reference surfaces of a tool or artefact mounted on the first member and multiple reference surfaces of an artefact mounted on the second member. At least one of the model parameters is updated knowing or taking into account that the actual separations between the relevant surfaces are zero when making contact, even if the expected separations between the relevant surfaces as derived from the current model parameters are non-zero.