New methods have been developed to implement high-resolution position sensors based on electron tunneling. These methods allow miniaturization while utilizing the position sensitivity of electron tunneling to give high resolution. A single-element tunneling accelerometer giving a displacement resolution of 2×10-3 angstroms/√Hz at 10 Hz, corresponding to an acceleration resolution of 5×10-8 g/√Hz, is described. A new dual-element tunneling structure which overcomes the narrow bandwidth limitations of a single-element structure is described. A sensor with an operating range of 5 Hz to 10 kHz, which can have applications as an acoustic sensor, is discussed. Noise is analyzed for fundamental thermal vibration of the suspended masses and is compared to electronic noise. It is shown that miniature tunnel accelerometers can achieve resolution such that thermal noise in the suspended masses is the dominant cause of the resolution limit. With a proof mass of order 100 mg, noise analysis predicts limiting resolutions approaching 10-9 g/√Hz in a 300 Hz band and 10-8 g/√Hz at 1 kHz.