Uncertainties in contact dynamics and object geometry remain significant barriers to robust robotic manipulation. Caging helps mitigate these uncertainties by constraining an object's mobility without requiring precise contact modeling. Existing caging research often treats morphology and policy optimization as separate problems, overlooking their synergy. In this paper, we introduce CageCoOpt, a hierarchical framework that jointly optimizes manipulator morphology and control policy for robust caging-based manipulation. The framework employs reinforcement learning for policy optimization at the lower level and multitask Bayesian optimization for morphology optimization at the upper level. We incorporate a caging metric into both optimization levels to encourage caging configurations and thereby improve manipulation robustness. The evaluation consists of four manipulation tasks and demonstrates that co-optimizing morphology and policy improves task performance under uncertainties, establishing caging-guided co-optimization as a viable approach for robust manipulation.