Engineering solutions based on dynamical chaos may improve the characteristics of various sensors such as metal detectors, salinometers, optical and magnetic field sensors, and so on. In this study, we investigated the possibility of creating inductive sensors based on Sprott chaotic oscillators with a planar printed circuit board inductive coil. The electric circuit of each sensor was obtained by merging two parts, namely, a harmonic oscillator and a nonlinear filter. A novel method for real-time oscillation analysis using a bandpass filter is presented. The suggested design technique was experimentally validated, and the sensor prototype showed characteristics making it practically applicable. In addition, the proposed technique can be used for the development of other types of sensors based on chaotic oscillators.