We consider component-wise estimation of order restricted location/scale parameters of a general bivariate location/scale distribution under the generalized Pitman nearness criterion (GPN). We develop some general results that, in many situations, are useful in finding improvements over location/scale equivariant estimators. In particular, under certain conditions, these general results provide improvements over the unrestricted Pitman nearest location/scale equivariant estimators and restricted maximum likelihood estimators. The usefulness of the obtained results is illustrated through their applications to specific probability models. A simulation study has been considered to compare how well different estimators perform under the GPN criterion with a specific loss function.