Beam lines magnets for high rigidity particles can have a large power dissipation. In presence of a high duty cycle, this translates in a considerable amount of energy waste. The call for sustainability of large research infrastructures, like particle accelerator centers, and the recent increase of the cost of energy, require to take measures to reduce the energy consumption, even at cost of moderate investment. A study program called ESABLIM (Energy SAving Beam LIne Magnets) has been set up at the LASA lab of University and INFN Milano, aimed at revamping existing normal-conducting magnets for beam lines with the target of cutting the peak power by a factor 10 to 20 and reducing the energy consumption by factor 5 or more. The idea is to replace the water cooled coils of iron-dominated magnets with new superconducting coils cooled at 10-20 K by means of a cryocooler, while to reusing the iron yoke pole assembly. We envisage using MgB2 for its moderate cost, however, high temperature superconductors (HTS) will also be considered as conductor. We present the first advanced design for revamping of a large bending dipole in a hadron therapy center, and the conceptual design for magnets in a nuclear physics laboratory and we try to define the domain where this transformation of normal-conducting into super-ferric magnets can be technically and economically advantageous.