Our goal is to bridge free-material optimization (FMO) with microstructural realizability. To do so, we first tighten the traditional FMO problem by replacing the local and global trace constraints using a volume estimator constructed using Voigt bounds. The resulting problem (FMO-V) is still a convex optimization problem, but turns out to be equivalent to the well known VTS problem. We thus continue to further tighten the feasible set using Hashin–Shtrikman (HS) energy bounds, which are known to be tight for for the single-load compliance minimization case. We prove non-convexity of the feasible set for the resulting (FMO-HS) problem and show that its closed convex hull coincides with the feasible set of (FMO-V). As the minimum for the (FMO-HS) constrained problem is attained by an orthotropic material distribution, we further introduce the Free Orthotropic Material Optimization (FOMO-HS) problem, for which the volume estimator based on HS bounds can be considerably simplified. We demonstrate how this problem can be approximately solved by the sequential global programming (SGP) approach. Despite the non-convex nature of (FOMO-HS), comparisons to an approach by Allaire based on finite rank laminates reveal that SGP solutions are competitive. While these comparisons are limited to the single load case, the SGP method is also applicable in the multiple load case. In a last step, we numerically validate the (FOMO-HS) predictions using a catalog of manufacturable orthotropic microstructures constructed by inverse homogenization. We solve the resulting material optimization problem over the catalogue by a variant of the SGP method. Beyond this validation, we study the cost of connectivity of the micro-structure by numerical experiments. In summary, our approach links abstract FMO problems to realizable, compatible microstructures across single- and multi-load settings.