The increasing prevalence of elemental thermocouples, Au/Pt and Pt/Pd, in place of those using alloys of platinum and rhodium, has dramatically reduced measurement uncertainties at temperatures above the range of platinum resistance thermometers, to the extent that the single largest contribution to the uncertainty budget is often that due to the inhomogeneity of the Seebeck coefficient in the thermoelements along the length. This uncertainty must be estimated as an upper limit because the temperature gradient experienced by the thermocouple during calibration may be very different to that used in the field. In the worst case uncertainties of hundreds of mK are possible, although often the profiles are quite similar and the uncertainties are much lower than this. Here a method is presented for quantitatively determining the uncertainty in emf arising from inhomogeneity, by employing an experimentally determined sensitivity as a function of distance along the thermocouple, and numerically evaluating the effect of this sensitivity by considering its influence on all possible linear temperature gradients that the thermocouple can experience. It is then possible to determine the uncertainty due to the inhomogeneity within a desired confidence interval.