Resonant light scattering by mesoscale dielectric spheres has received enormous attention and found many interesting applications. The recently emerged field of Mesotronics provides novel opportunities for wavelength‐scaled optics and new fundamental aspects are still being uncovered. It has recently been demonstrated that high‐order Mie resonances can be excited in homogeneous low‐dissipation mesoscale dielectric spheres, leading to the generation of intense magnetic fields. This article describes a simple and effective way to drastically enhance the superresonance effect. Proof‐of‐principle results for the first time show that yet one more novel phenomenon of increasing the intensity of the magnetic field without changing the resonant Mie size parameter of the sphere by introducing an air cavity. In such a dielectric cenosphere (from two Greek words “kenos”‐hollow and “sphaira”‐sphere), by correct choice of the air cavity size, it is possible to increase the intensity of the electromagnetic fields at the poles of the sphere by an order of magnitude due to increasing of the amplitude of resonant partial wave coefficient.