An electronic article surveillance (EAS) tag/device with coplanar and/or multiple coil circuits, a tag/device with two or more memory bits, and methods for making and tuning the resonant frequency of an EAS tag/device. The device generally includes: an outer inductor having one end coupled to a capacitor plate; an inner inductor having one end coupled to an other capacitor plate; a first dielectric film on the outer and inner inductors and the capacitor plates coupled thereto, having openings therein exposing other ends of the outer and inner inductors; a linear capacitor plate and a nonlinear capacitor plate on the first dielectric film; a second dielectric film containing holes therein for the second linear and nonlinear capacitor plates, and exposing the other ends of the first and second inductors; and first and second conducting straps on the second dielectric film, electrically connecting one of the exposed inductor ends to a corresponding second capacitor plate.