Anomalous field enhancement accompanied by resonant absorption phenomenon was originally discussed in the context of plasma physics and in applications related to radio-communications between the ground and spacecraft returning to Earth. Indeed, there is a critical period of time when all communications are lost due to the reflection/absorption of electromagnetic waves by the sheath of plasma created by a high speed vehicle re-entering the atmosphere. While detailed experimental studies of these phenomena in space are challenging, the emergence of electromagnetic metamaterials enables researchers exceptional flexibility to study them in the laboratory environment. Here, we experimentally demonstrated the strong localized field enhancement of magnetic field for an electromagnetic wave propagating in Mie-resonance-based inhomogeneous metamaterials with magnetic permeability gradually changing from positive to negative values. Although these experiments were performed in the microwave frequency range, the proposed all-dielectric approach to transition metamaterials can be extended to terahertz, infrared, and visible frequencies. We anticipate that these results, besides most basic science aspects, hold the potential for numerous applications, including low-intensity nonlinear transformation optics, topological photonics, and the broader area of surface and interface science.