As an aquatic locomotion strategy, metachronal paddling is used by organisms across a wide number of distantly related taxa. The broad diversity of body and appendage morphologies of metachronal swimmers make it difficult to generalize how specific morphological and kinematic parameters impact swimming performance. Biorobotics approaches can be particularly useful in this context to synthesize physical design principles underlying this successful locomotion strategy. We summarize our studies using tethered and self-propelling dynamically scaled robotic models of metachronal paddling to address the following questions: (1) How do negatively buoyant crustaceans generate downward momentum to support their weight while hovering? (2) How does varying the distance between neighboring appendages affect swimming performance? (3) How does varying stroke kinematics (inter-appendage phase lag) affect swimming performance? We use quantitative flow visualization measurements to identify physical mechanisms that explain the observed changes in swimming speed. We find that hydrodynamic interaction of the wakes of closely spaced paddles can increase forward swimming speed. Paddling with a non-zero phase lag promotes the formation of counter-rotating vortices, and their interaction results in generation of large-scale angled downward jets that can provide vertical momentum necessary to support body weight during hovering. The use of a metachronal power stroke followed by a synchronous recovery stroke allows for large stroke amplitudes even with close appendage spacing, resulting in an appreciable increase in swimming speed. This pattern of hybrid stroke kinematics is seen in escaping copepods and mantis shrimp, and serves as an example of how the metachronal propulsion system can be adapted for a range of behavioral and ecological needs.