In this paper, we apply evolutionary multiobjective optimization to the design of a robotic fish with a flexible caudal fin. Specifically, we use the NSGA-II algorithm to discover solutions (physical dimensions, flexibility, and control parameters) that optimize both swimming performance and power efficiency. The optimization is conducted in a custom simulation environment based on an accurate yet computationally-efficient model of hydrodynamics. The results of these simulations reveal general principles that can be applied in the design of robotic fish morphology and control. To verify that the simulation results are physically relevant, we selected several of the evolved solutions, fabricated flexible caudal fins using a multi-material 3D printer, and attached them to a robotic fish prototype. Experimental results, conducted in a large water tank, correspond reasonably well to simulation results in both swimming performance and power efficiency, demonstrating the usefulness of evolutionary computation methods to this application domain.