Unilateral degrees of equivalence are the key result in the analysis of key comparison data and they are used to approve, or disapprove, calibration and measurement capabilities of the participating laboratories. To this end, it is checked whether a degree of equivalence differs significantly from zero. Proceeding in such a way can be viewed as carrying out a classical hypothesis test. We develop a Bayesian counterpart to this approach which has the advantage that it can include prior assessment of the corresponding Consultative Committee about the calibration and measurement capabilities of the participating laboratories. Simple expressions are derived and their implementation is provided in terms of MATLAB® and R programs. The novel procedure is illustrated by its application to two recent key comparisons CCL-K1 and CCM.FF-K4.1.2011.