We present a novel efficient technique for the analysis of inductive structures containing metallic and dielectric obstacles, using a Surface Integral Equation (IE) formulation. Using the Surface Equivalence Principle, the main problem is divided into two subproblems. The first one is formulated with the parallel plate waveguide (PPW) Green's functions, and the second with the Green's functions of an unbounded homogeneous medium. The most important contribution of this paper is the consideration of obstacles attached to the waveguide walls. This situation requires a special treatment of the Green's functions of the second subproblem, by adding a spatial image with respect to the corresponding wall where the attachment is placed. This is essential in order to obtain adequate results, as it will be shown in further examples. Moreover, the presence of inductive dielectric posts connected to the walls inside cavity filters allows to obtain interesting elliptic responses, in addition to the possibility of reducing the multipactor risk for space applications.