  A method based on multicanonical Monte Carlo is applied to the calculation of
large deviations in the largest eigenvalue of random matrices. The method is
successfully tested with the Gaussian orthogonal ensemble (GOE), sparse random
matrices, and matrices whose components are subject to uniform density.
Specifically, the probability that all eigenvalues of a matrix are negative is
estimated in these cases down to the values of $\sim 10^{-200}$, a region where
naive random sampling is ineffective. The method can be applied to any ensemble
of matrices and used for sampling rare events characterized by any statistics.
