We study the electromagnetic Casimir interaction of a metallic compact object with a compact and bounded metallic surface in which it is contained. We express the interaction energy in terms of the objects' scattering matrices and translation matrices that relate the coordinate systems appropriate to each object. In the large spherical shell limit, the Casimir energy can be expressed in terms of the static electric and magnetic multi-pole polarizabilities of the inner object, which is the interior analog of the Casimir-Polder result, although it does not have a simple power law dependence on the separation of the object from the containing surface. Additionally, we compute the exact Casimir force between two metallic spheres contained one inside the other for arbitrary separations. Finally, we combine our results with earlier work on the Casimir force between two spheres to obtain data on the first order correction to the Proximity Force Approximation for two metallic spheres both outside and within one another.