Tow-steered variable angle tow (VAT) fiber composites are advantageous in structural design as they allow stiffness tailoring. However, designing this new material is challenging due to the large design space resulting from the variable angle fiber path parameterization. The suitability of Parametric Model Order Reduction (PMOR) for improving the efficiency of structural optimization with frequency constraints was investigated by applying it to two different problems: (1) truss topology optimization formulated as a semidefinite programming (SDP) problem and (2) buckling load maximization of a VAT plate, solved using Particle Swarm Optimization (PSO). It was found that the PMOR-based PSO was more amenable to our design goal, and the efficiency can be significantly improved using affine decompositions of the system matrices. Another challenging aspect of the design process is the implementation of manufacturing constraints on the tow paths to obtain practically feasible designs. A B-spline-based constraint definition is discussed.