The assessment of the Metop-SG microwave imager radiometric performance is based on a complete set of thermal vacuum tests. Such an extensive experimental campaign requires the development of large calibration targets (black bodies) with controlled systematics and low residual uncertainties. The significant size of such targets, which are based on pyramidal emitting surfaces, does not allow for a complete minimization of the thermal gradients below the required accuracy level. This article presents the modeling approach that has been developed to deal with both such thermal gradients and the proximity of the baffle. Results on the frequency dependence of the cold target brightness temperature (ECCOSORB CR-117) are reported between 18.7 and 183 GHz. The complete uncertainty budget provides 1-sigma errors levels lower than 0.22 K. The systematic effect of thermal coupling with the earth target has been found as relevant as the coupling to the chamber. This interdependence requires a look-up-table approach to maintain the low uncertainty levels mentioned above.