We introduce and implement an importance-sampling Monte Carlo algorithm to study systems of globally-coupled oscillators. Our computational method efficiently obtains estimates of the tails of the distribution of various measures of dynamical trajectories corresponding to states occurring with (exponentially) small probabilities. We demonstrate the general validity of our results by applying the method to two contrasting cases: the driven-dissipative Kuramoto model, a paradigm in the study of spontaneous synchronization; and the conservative Hamiltonian mean-field model, a prototypical system of long-range interactions. We present results for the distribution of the finite-time Lyapunov exponent and a time-averaged order parameter. Among other features, our results show most notably that the distributions exhibit a vanishing standard deviation but a skewness that is increasing in magnitude with the number of oscillators, implying that non-trivial asymmetries and states yielding rare/atypical values of the observables persist even for a large number of oscillators.
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