We propose a soft electromagnetic sliding actuator that provides various planar motions to construct highly compliant actuation systems. The actuator is composed of a fully soft actuation base (stator) for generating electromagnetic and magnetic forces and a rigid neodymium magnet (slider) that slides on the actuation base. A parallel liquid-metal coil array in the stator is designed based on theoretical modeling and an optimization process to maximize the electromagnetic field density. The stretchable magnetic components in the stator allow the slider to retain its position stably without additional constraints. By incorporating an untethered structure in which the slider is mechanically decoupled from the stator, the actuator can be operated with reduced power consumption, attributed to the absence of a restoring force. The trajectory of the slider can be programmed by selectively applying the input current to the liquid-meal coil array, and the location of the slider can be estimated by measuring the change in inductance of each coil. Moreover, the proposed actuator demonstrates the capability of operating on curved surfaces through its physical compliance as well as on inclined surfaces thanks to the holding force generated by the magnetic components of the stator. Taking advantage of the unique characteristics of our actuator, robotic applications, including shape morphing systems and sensor-actuator integrated systems, are demonstrated.