Several important preconditioners for saddle point problems yield linear systems for which the GMRES iterative method converges exactly in just a few iterations. However, these preconditioners all involve inverses of large submatrices. In practical computations such inverses are only approximated, and more iterations are required to solve the preconditioned linear system. How many more iterations? In this talk, we present perturbation analysis results for GMRES that leads to rigorous upper bounds on the number of iterations as a function of the accuracy of the preconditioner to the ideal and spectral properties of the constituent matrices. We also derive a thorough analysis of the spectral properties of these common saddle point preconditioners. Generalizations of these preconditioners have been proposed, however their convergence properties have not been described. Our spectral analysis of these generalized systems allow us to finally prove tight convergence bounds for these preconditioned systems.