Nonlinear eigenvalue problems occur naturally when looking at differential equation models that include damping, radiation, or delay effects. Such problems also arise when we reduce a linear eigenvalue problem, as occurs when we rewrite a PDE eigenvalue problem in terms of a boundary integral equation. In each of these cases, we are interested in studying the zeros of a meromorphic matrix-valued function A : C → Cn×n. In this talk, we describe extensions of some standard perturbation results and bounds for nonlinear eigenvalue problems, and apply these results to error estimates for computing resonances and eigenvalues of Schrödinger operators.