During the excitation of high-temperature superconducting (HTS) magnets, traditional contact-type lead power supply must traverse from room temperature to cryogenic temperatures, generating significant Joule heat and forming a heat leakage source, which reduces the thermal stability and reliability of the magnet. To address this issue, this paper leverages the inherent zero-resistance/flux-flow resistance transition property of HTS materials and proposes a wireless power supply method for HTS magnets based on self-driven bridge synergy, with a focus on studying its through-wall excitation performance. A finite element model of a normal-conducting/superconducting hybrid electromagnetic coupling mechanism was constructed, and the coupling efficiency between the primary and secondary sides was improved by incorporating magnetic conductive materials. And an experimental platform for wireless power supply of a levitated HTS magnet was established, achieving an excitation current of 52 A across a 12 mm metal container wall, validating the effectiveness of the proposed power supply method. This work lays a theoretical foundation for advancing wireless power supply technologies for HTS magnets.