To develop robust manipulation policies, quantifying robustness is essential. Evaluating robustness in general manipulation, nonetheless, poses significant challenges due to complex hybrid dynamics, combinatorial explosion of possible contact interactions, global geometry, etc. This paper introduces an approach for evaluating manipulation robustness through energy margins and caging-based analysis. Our method assesses manipulation robustness by measuring the energy margin to failure and extends traditional caging concepts for dynamic manipulation. This global analysis is facilitated by a kinodynamic planning framework that naturally integrates global geometry, contact changes, and robot compliance. We validate the effectiveness of our approach in simulation and real-world experiments of multiple dynamic manipulation scenarios, highlighting its potential to predict manipulation success and robustness.