We describe a novel single-coil mutual inductance technique for measuring the magnetic penetration depth lambda of superconductors at 2-4 MHz as a function of temperature in the 4-100 K range. We combine a single-coil configuration with a high-stability marginal oscillator; this enables us to measure the absolute value of lambda on both bulk samples and thin films with very high resolution (delta lambda=10 pm) and a precision of 30 nm. As example of application, we report measurements on NbTi bulk samples and Nb films. This contactless technique is suited for probing the superconducting properties of samples over large surfaces.