Soft electromagnetic artificial muscles (SEAMs) that use electric currents are reported as their power sources. The proposed actuator consists of fully soft components: microfluidic coils, stretchable magnets, ferromagnetic silicone, and stretchable housings. The soft coils are fabricated by directly printing room-temperature liquid metal on a stretchable substrate, enabling the generation of high-density electromagnetic fields. Based on design optimization through modeling and simulation, the proposed actuators have a characteristic of bistability following the relationships of the forces acting on the components. Depending on the design configurations, the proposed actuators generate contraction and expansion motions as well as vibrations in a bidirectional manner, enabled by electromagnetic actuation. The main advantages of the proposed actuators are fully compliant structures, compact form factors, and short response times, which have not been observed in existing polymer-based artificial muscles. Another advantage is the self-detection of the actuation states by measuring the inductance change in the coils. Last, the modular design fully packaged with a coil and magnets in a soft housing makes it possible to easily resize and reconfigure the robotic systems with multiple actuator modules for different applications. Examples of applications demonstrated are a modular crawling robot, energy-efficient grippers, a multi-degrees of freedom (DOF) soft manipulator, and a high-frequency swimming robot.