Abstract: Supersymmetric mass spectra within two variants of the seesaw mechanism, commonly known as type-II and type-III seesaw, are calculated using full 2-loop RGEs and minimal Supergravity boundary conditions. The type-II seesaw is realized using one pair of 15 and (15) over bar superfields, while the type-III is realized using three copies of 24(M) superfields. Using published, estimated errors on SUSY mass observables attainable at the LHC and in a combined LHC+ILC analysis, we calculate expected errors for the parameters of the models, most notably the seesaw scale. If SUSY particles are within the reach of the ILC, pure mSugra can be distinguished from mSugra plus type-II or type-III seesaw for nearly all relevant values of the seesaw scale. Even in the case when only the much less accurate LHC measurements are used, we find that indications for the seesaw can be found in favourable parts of the parameter space. Since our conclusions crucially depend on the reliability of the theoretically forecasted error bars, we discuss in some detail the accuracies which need to be achieved for the most important LHC and ILC observables before an analysis, such as the one presented here, can find any hints for type-II or type-III seesaw in SUSY spectra.