A new approach to the prediction of protein structures that uses distance and backbone virtual-bond dihedral angle restraints derived from template-based models and simulations with the united residue (UNRES) force field is proposed. The approach combines the accuracy and reliability of template-based methods for the segments of the target sequence with high similarity to those having known structures with the ability of UNRES to pack the domains correctly. Multiplexed replica-exchange molecular dynamics with restraints derived from template-based models of a given target, in which each restraint is weighted according to the accuracy of the prediction of the corresponding section of the molecule, is used to search the conformational space, and the weighted histogram analysis method and cluster analysis are applied to determine the families of the most probable conformations, from which candidate predictions are selected. To test the capability of the method to recover template-based models from restraints, five single-domain proteins with structures that have been well-predicted by template-based methods were used; it was found that the resulting structures were of the same quality as the best of the original models. To assess whether the new approach can improve template-based predictions with incorrectly predicted domain packing, four such targets were selected from the CASP10 targets; for three of them the new approach resulted in significantly better predictions compared with the original template-based models. The new approach can be used to predict the structures of proteins for which good templates can be found for sections of the sequence or an overall good template can be found for the entire sequence but the prediction quality is remarkably weaker in putative domain-linker regions.