A method of forming an actuator and a relay using a micro-electromechanical (MEMS)-based process is disclosed. The method first forms the lower sections of a square copper coil, and then forms an actuation member that includes a core section and a horizontally adjacent floating cantilever section. The core section, which lies directly over the lower coil sections, is electrically isolated from the lower coil sections. The method next forms the side and upper sections of the coil, along with first and second electrodes that are separated by a switch gap. The first electrode lies directly over an end of the core section, while the second electrode lies directly over an end of the floating cantilever section.