In this research we develop a mathematical construct for estimating uncertainties within the bilevel optimization framework of collaborative optimization. The collaborative optimization strategy employs decomposition techniques that decouple analysis tools in order to facilitate disciplinary autonomy and parallel execution. To ensure consistency of the physical artifact being designed, interdisciplinary consistency constraints are introduced at the system level. These constraints implicitly enforce multidisciplinary consistency when satisfied. The decomposition employed in collaborative optimization prevents the use of explicit propagation techniques for estimating uncertainties of system performance. In this investigation, we develop and evaluate an implicit method for estimating system performance uncertainties within the collaborative optimization framework. The methodology accounts for both the uncertainty associated with design inputs and the uncertainty of performance predictions from other disciplinary simulation tools. These implicit uncertainty estimates are used as the basis for a new robust collaborative optimization (RCO) framework. The bilevel robust optimization strategy developed in this research provides for disciplinary autonomy in system design, while simultaneously accounting for performance uncertainties to ensure feasible robustness of the resulting system. The method is effective in locating a feasible robust optimum in application studies involving a multidisciplinary aircraft concept sizing problem. The system-level consistency constraint formulation used in this investigation avoids the computational difficulties normally associated with convergence in collaborative optimization. The consistency constraints are formulated to have the inherent properties necessary for convergence of general nonconvex problems when performing collaborative optimization.