Using the Meissner effect in superconductors, demonstrated here is the capability to create an arbitrarily high magnetic flux density (also sometimes referred to as “flux squeezing”). This technique has immediate applications for numerous technologies. For example, it allows the generation of very large magnetic fields (e.g., exceeding 1 Tesla) for nuclear magnetic resonance (NMR), magnetic resonance imaging (MRI), the generation of controlled magnetic fields for advanced superconducting quantum computing devices, and/or the like. The magnetic field concentration/increased flux density approaches can be applied to both static magnetic fields (i.e., direct current (DC) magnetic fields) and time-varying magnetic fields (i.e., alternating current (AC) magnetic fields) up to microwave frequencies.