Coarse-grained elastic network models (ENM) of proteins can be used efficiently to explore the global mobility of a protein around a reference structure. A new Hamiltonian-replica exchange molecular dynamics (H-RexMD) method has been designed that effectively combines information extracted from an ENM analysis with atomic-resolution MD simulations. The ENM analysis is used to construct a distance-dependent penalty (flooding or biasing) potential that can drive the structure away from its current conformation in directions compatible with the ENM model. Various levels of the penalty or biasing potential are added to the force field description of the MD simulation along the replica coordinate. One replica runs at the original force field. By focusing the penalty potential on the relevant soft degrees of freedom the method avoids the rapid increase of the replica number with increasing system size to cover a desired temperature range in conventional (temperature) RexMD simulations. The application to domain motions in lysozyme of bacteriophage T4 and to peptide folding indicates significantly improved conformational sampling compared to conventional MD simulations.