Despite the fact that quantum gravity is non-renormalisable, a consistent and mathematically rigorous construction of a perturbation series is possible. This is based on the use of the Batalin-Vilkovisky-Becchi-Rouet-Stora-Tyutin formalism for gauge theories, the methods of perturbative algebraic quantum field theory and the principle of local covariance. The truncation of the series can be interpreted as an effective quantum field theory which provides predictions for observations at sufficiently small energy scales. Quantum cosmology can be seen as its lowest order expansion, and precision measurements on the cosmic microwave background yield the first empirical test of this approach to quantum gravity.