We derive a lower bound on the sensitivity of generic mechanical and electromagnetic gravitational wave detectors. We consider both classical and quantum detection schemes, although we focus on the former. Our results allow for a simple reproduction of the sensitivities of a variety of experiments, including optical interferometers, resonant bars, optomechanical sensors, and electromagnetic conversion experiments. In the high-frequency regime, all detection schemes we consider can be characterised by their stored electromagnetic energy and the signal transfer function, which we provide. We discuss why high-frequency gravitational wave searches are especially difficult and primordial gravitational wave backgrounds might not be detectable above the sensitivity window of existing interferometers.