The use of lattices and microstructures in geometric design have been recognized as potentially superior to solid structures due to the potential benefits in improved strength-to-weight ratios, better control over heat exchange and heat transfer, and so on. In this work, we present a construction scheme to create parametric microstructures in a boundary representation (B-rep) model, M, that are conformal to an arbitrary specification, including the boundary of M. Given a B-rep model, M, either a polygonal or trimmed-spline based, a cage, T, is constructed around M to guide the synthesis of the microstructures in M. Micro-elements are synthesized following T, and verified to be inside M while bridging tiles are added as necessary. These parametric micro-elements can be heterogeneous in their material content, as well as locally vary in their geometric properties. We demonstrate these abilities with example microstructures synthesized from both polygonal B-rep models and spline-based B-rep solids, including 3D printed parts.