Aerodynamic balances are employed in wind tunnels to estimate the forces and moments acting on the model under test. This paper proposes a methodology for the assessment of uncertainty in the calibration of an internal multi-component aerodynamic balance. In order to obtain a suitable model to provide aerodynamic loads from the balance sensor responses, a calibration is performed prior to the tests by applying known weights to the balance. A multivariate polynomial fitting by the least squares method is used to interpolate the calibration data points. The uncertainties of both the applied loads and the readings of the sensors are considered in the regression. The data reduction includes the estimation of the calibration coefficients, the predicted values of the load components and their corresponding uncertainties, as well as the goodness of fit.