With the resurgent interest in landing humans on Mars, it is critical that our understanding of the Martian environment is complete and accurate. One way to improve our model of the red planet is through aerial surveillance, which provides information that augments the observations made by ground-based exploration and satellite imagery. Although the ultra-low-density Mars environment has previously stymied designs for achieving flight on Mars, bioinspired solutions for flapping wing flight can utilize the same high lift producing mechanisms employed by insects on Earth. Motivated by the current technologies for terrestrial flapping wing aerial vehicles on Earth, we seek solutions for a 5 gram bioinspired flapping wing aerial vehicle for flight on Mars. A zeroth-order method is proposed to determine approximate wing and kinematic values that generate bioinspired hover solutions. We demonstrate that a family of solutions exists for designs that are O(101) g, which are verified using a 3D Navier-Stokes solver. Our results show that unsteady lift enhancement mechanisms, such as delayed stall and rotational lift, are present in the bioinspired solution for a 5 g flapping wing vehicle hovering in Mars conditions, verifying that the zeroth-order method is a useful design tool. As a result, it is possible to design a family of bioinspired flapping wing robots for Mars by augmenting the adverse effects of the ultra-low density with large wings that exploit the advantages of unsteady lift enhancement mechanisms used by insects on Earth.