Our planet urges for a more responsible use of its resources, and since information technology contributes substantially to the global energy consumption, software engineering research has promptly embraced this request and is actively working towards more sustainable processes. An indispensable activity in software development is testing, which is known to be very costly in terms of time and effort. On top of this, a recent study by Zaidman has shown that software testing can be a voracious energy consumer as well. In this work we introduce the very concept of energy-aware testing as the adoption of ad hoc strategies that can help reduce the energy consumption of existing practices. We discuss some possible strategies and, as an example, we conduct a first study of an energy-aware variant of a simple similarity-based test prioritization approach, which provides evidence of perceptible savings. We encourage future research in energy-aware software testing that need to address further studies and to think up more strategies.