approach in that the uncertainty evaluation can only be performed after the experimental results. The second approach, as described by the Guide to the Expression of Uncertainty in Measurement (GUM, [3; 9; 10], is model-based and relies on an input-output model that describes the measurement result as a known function of the influence factors. Assigning means and variances (and distributions) to the influence factors allows, in principle, means and variances (and distributions) associated with the measurand to be estimated. The two approaches to uncertainty evaluation associated with coordinate metrology were addressed by a recent European project _Evaluation of uncertainty associated with coordinate metrology_--EUCoM; [11]. The first, observation-based approach is based on taking multiple measurements of the same artefact in a number of positions within the working volume of the CMM, specifically, five repeat measurements in each of four positions. This approach is designed to assess the repeatability component of uncertainty, along with the effect of the geometric errors of the CMM that vary with location within the working volume. An analysis of variance approach is used to assess the uncertainty contributions from repeatability and the geometric errors [12; 13]. This paper is concerned with a model-based approach to evaluating CMM uncertainty. The virtual CMM (VCMM) concept, see, e.g., [14; 15; 16; 17; 18; 19], is an established example of a model-based approach for CMM uncertainty evaluation. The VCMM approach involves (i) a comprehensive model of the CMM behaviour, including the kinematic errors, involving the order of 100 or more model parameters, (ii) a detailed statistical characterisation of the model parameters, and (iii) a Monte Carlo approach [9; 10] for propagating the uncertainties associated with the model parameters through to the features derived from the point cloud data. While the VCMM approach potentially is the method of choice for CMM uncertainty evaluation, it does suffer from a number of drawbacks: (a) it requires a large number of parameters to be characterised statistically, often through extensive measurement exercises involving multiple measurements of artefacts such as ball plates [20; 21; 22], (b) the statistical characterisation of the parameters may not reflect the behaviour of the CMM at later times or in different environments, and (c) there is considerable computation required to implement this in software. The approach described in this paper and developed during the EUCoM project follows a model-based approach, as used in the VCMM methodology, but with two simplifications. The first exploits the fact that the dependence of the measured point coordinates \(\mathbf{x}_{i}\) on the influence factors can be modelled explicitly, which enables the sensitivity with respect to the influence factors to be determined analytically (to the first order). The sensitivity of derived features such as distances and differences in distances can also be determined analytically. The second simplification is to employ approximate models of CMM kinematic errors and probing effects based on Gaussian process models [23]. The models are approximate in the sense that in the absence of information about the actual kinematic or probing errors, the models describe plausible behaviour of the CMM. We also note that these models apply to CMMs that are assumed to be error-corrected already so that the models are required to describe the departure of the CMM's actual behaviour from its modelled behaviour rather than account for the kinematic and probing errors themselves. The models are being used to estimate the uncertainty contributions from the various influence factors, not to evaluate or estimate (and correct for) the influence factors themselves. This means that some of the complexity of error correction can be avoided.