Precision is a crucial property of noisy circadian oscillators that can be quantified by the quality factor (Q). Until now, deterministic properties of circadian oscillations like the period or amplitude attracted most of the attention while relatively few studies addressed the problem of assessing Q. One reason is that Q is more difficult to access experimentally and even theoretically. The main objective of this thesis is to provide methods to efficiently estimate Q both in experimental data of cell-autonomous circadian oscillations and stochastic models. First a theoretical study, in an effort to unify existing low noise approximations of Q with different domains of validity near or away of Hopf bifurcations (HBs), shows that the link between the two cases lies in the projection of the Langevin Equation onto the phase gradient vector. Furthermore we formulate both approximations in a way that permits application to generic oscillator models undergoing HBs and applied them to a 16-dimensional circadian model. We find that as the noise increases, the precision of oscillations of individual chemical species and agreement with the global precision predicted by the low noise approximations, become species dependent. In a second part we first discuss in detail which methods, based on our theoretic study, are best suited to reliably estimate Q for different types of experimental data. Comparing the simple brownian phase model with single cell resolution bioluminescence data, we then support the assumption, that it is reasonable to consider different cells as identical oscillators. This allows to compensate the relatively short time scales available in experimental data by sampling many different cells. Then we extend existing software to accurately track bioluminescence emitting mammalian cells, subjected to different conditions of reduced transcription rates, and, taking advantage of the methods that we elaborated, estimate Q. Comparing this additional information to the prediction of the minimal Normal Form model we arrive at the conclusion that these noisy oscillators are operating in a self-sustained rather than damped regime. This work yields a better understanding of how molecular noise affects the precision of biochemical oscillators and has important implications for the interpretation and design of experiments aimed at measuring the precision of molecular oscillators.