Robustness analysis assesses the performance of a particular solution under variation in the input data. This is distinct from sensitivity analysis, which assesses how variation in the input data changes a model's optimal solution. For risk assessment purposes, robustness analysis has more practical value than sensitivity analysis. This is because sensitivity analysis, when applied to optimization models, assumes that the solution is able to adapt to changes in the input data with perfect foresight, which may lead to an overly optimistic assessment. On the other hand, classical robustness analysis, which is intended for static optimization problems, assumes that the solution is entirely fixed and unable to adapt to changes in the input data, which may lead to an overly pessimistic assessment. In this paper we extend robustness analysis to deal with adaptive optimization problems in a more realistic manner. Furthermore, we propose an intuitive and computationally tractable method for applying robustness analysis to adaptive optimization problems and apply this method to the optimization of decarbonization pathways for heavy industry in the Netherlands. Here we find significant differences between the results obtained via (i) sensitivity analysis, (ii) classical robustness analysis (for static optimization) and (iii) robustness analysis for adaptive optimization. Our results demonstrate the importance of the methodology when analyzing the impact of uncertainty.