Context. The phase of radio galaxy evolution after the jets have switched off, often referred to as the remnant phase, is poorly understood and very few sources in this phase are known. Aims: In this work we present an extensive search for remnant radio galaxies in the Lockman Hole, a well-studied extragalactic field. We create mock catalogues of low-power radio galaxies based on Monte Carlo simulations to derive first-order predictions of the fraction of remnants in radio flux limited samples for comparison with our Lockman-Hole sample. Methods: Our search for remnant radio galaxies is based on LOFAR observations at 150 MHz combined with public survey data at higher frequencies. To enhance the selection process, and obtain a more complete ...