We provide error bound results for Karush–Kuhn–Tucker systems of mathematical programs with complementarity constraints (MPCC), reformulated as smooth and piecewise smooth constrained equations. These results are derived under mild assumptions not involving MPCC-LICQ, and for the piecewise smooth reformulation, not involving the upper level strict complementarity condition as well. Since error bounds serve as a key ingredient for achieving local superlinear convergence of Levenberg–Marquardt and LP-Newton methods, our findings justify the application of these methods to those constrained equations. We also provide numerical results supporting this approach, and in particular, demonstrating that the outcome of these methods can be reasonable not only from the viewpoint of convergence to strongly stationary points, but also by the achieved values of the objective function of the original optimization problem.