Superconductors have revolutionized magnet technology, surpassing the limitations of traditional coils and permanent magnets. This work experimentally investigates the field-trapping ability of a MgB2 disc at various temperatures and proposes new hybrid (MgB2-soft iron) configurations using a numerical approach based on the vector potential (A→) formulation. The experimental characterization consists in measurements of trapped magnetic flux density carried out using cryogenic Hall probes located at different radial positions over the MgB2 sample, after a field cooling (FC) process and the subsequent removal of the applied field. Measurements were performed also as a function of the distance from the disc surface. The numerical modelling of the superconductor required the evaluation of the critical current density dependence on the magnetic flux density (Jc(B)) obtained through an iterative procedure whose output were successfully validated by the comparison between experimental and computed data. The numerical model, upgraded to also describe the in-field behavior of ARMCO soft iron, was then employed to predict the field-trapping ability of hybrid layouts of different shapes. The most promising results were achieved by assuming a hollow superconducting disc filled with a ferromagnetic (FM) cylinder. With such a geometry, optimizing the radius of the FM cylinder while the external dimensions of the superconducting disc are kept unchanged, an improvement of more than 30% is predicted with respect to the full superconducting disc, assuming a working temperature of 20 K.