In this work a methodology is presented for the rigorous optimization of nonlinear programming problems in which the objective function and (or) some constraints are represented by noisy implicit black box functions. The special application considered is the optimization of modular process simulators in which the derivatives are not available and some unit operations introduce noise preventing the calculation of accurate derivatives. The black box modules are substituted by metamodels based on a kriging interpolation that assumes that the errors are not independent but a function of the independent variables. A Kriging metamodel uses non-Euclidean measure of distance to avoid sensitivity to the units of measure. It includes adjustable parameters that weigh the importance of each variable for obtaining a good model representation, and it allows calculating errors that can be used to establish stopping criteria and provide a solid base to deal with "possible infeasibility" due to inaccuracies in the metamodel representation of objective function and constraints. The algorithm continues with a refining stage and successive bound contraction in the domain of independent variables with or without kriging recalibration until an acceptable accuracy in the metamodel is obtained. The procedure is illustrated with several examples. (C) 2008 American Institute of Chemical Engineers.