To mitigate the effects of climate change, energy systems are becoming increasingly reliant on renewable energy sources. Since these energy sources are typically dependent on the prevailing weather, renewable energy systems are susceptible to shortages during certain weather conditions. As renewable sources become larger contributors to the energy mix, the risks associated with these shortages, referred to as energy droughts, increase. Techniques to monitor energy droughts are therefore required to mitigate the associated societal impacts. In this paper, two standardised indices are introduced to monitor droughts in renewable energy systems. The indices incorporate energy demand and renewable energy production, and constitute analogues of the standardised precipitation index (SPI) and standardised precipitation evapotranspiration index (SPEI), two indices regularly employed operationally to monitor meteorological droughts. The indices are straightforward to construct, can be defined on any timescale, and can readily be compared for regions with different climates and installed capacities. We demonstrate how the standardised energy indices proposed herein can be used to define renewable energy droughts, for which there is not yet a recognised definition. To illustrate the practical utility of these indices, they are applied to reconstructed time series of electricity demand and wind and solar power generation across Europe.