The paper deals with the constitutive relation error (CRE) concept which has been widely used over the last 40 years for verification and validation of computational mechanics models. It more specifically focuses on the beneficial use of model reduction based on proper generalized decomposition (PGD) into this CRE concept. Indeed, it is shown that a PGD formulation can facilitate the construction of so-called admissible fields which is a technical key-point of CRE. Numerical illustrations, addressing both model verification and model updating, are presented to assess the performances of the proposed approach.