Wearable electronics allow for new and immersive experiences between technology and the human body, but conventional devices are made from rigid functional components that lack the necessary compliance to safely interact with human tissue. Recently, liquid inclusions have been incorporated into elastomer composites to produce functional materials with high extensibility and ultrasoft mechanical responses. While these materials have shown high thermal and electrical conductivity, there has been an absence of research into compliant magnetic materials through the incorporation of magnetic fluids. Compliant magnetic materials are important for applications in soft matter engineering including sensing, actuation, and power transfer for soft electronics and robotics. In this work, we establish a new class of highly functional soft materials with advanced magnetic and mechanical properties by dispersing magnetic colloidal suspensions as compliant fluid inclusions into soft elastomers. Significantly, the rigid magnetic particles are encapsulated by the fluid. This mechanically cloaks the solid particles and enables a fluid-like mechanical response while imparting high magnetic permeability to the composite. This microstructure reduces the modulus of the composite below that of the initial elastomer to <40 kPa while increasing the permeability by over 100% to greater than 2. We demonstrate the functionality of these materials through conformable magnetic backplanes, which enables a completely soft, coupled inductor system capable of transferring power up to 100% strain and wearable devices for wireless power transfer.