Dielectric elastomer actuators (DEAs), a soft actuator technology, hold great promise for biomimetic underwater robots. The high-voltages required to drive DEAs can however make them challenging to use in water. This paper demonstrates a method to create DEA-based biomimetic swimming robots that operate reliably even in conductive liquids. We ensure the insulation of the high-voltage DEA electrodes without degrading actuation performance by laminating silicone layers. A fish and a jellyfish were fabricated and tested in water. The fish robot has a length of 120 mm and a mass of 3.8 g. The jellyfish robot has a 61 mm diameter for a mass of 2.6 g. The measured swimming speeds for a periodic 3 kV drive voltage were 8 mm/s for the fish robot, and 1.5 mm/s for the jellyfish robot.