The Bernstein-Sato polynomial is an important invariant of singularities, intimately related to the monodromy of the Milnor fiber, the log canonical threshold, and rational and Du Bois singularities. A classical method introduced by Kashiwara and refined by Lichtin provides estimates for the roots of the Bernstein-Sato polynomial in terms of a log resolution. In this talk, we extend their method to log resolutions by orbifolds, which has applications to the singularities of weighted homogeneous and Khovanskii non-degenerate complete intersections.