A fundamental issue in combinatorial optimization is determining how sensitive the solution of a problem is to perturbations in the input. Sensitivity analysis addresses this issue, but is limited to considering changes in the value of only a single element at a time. Instead, we focus in this talk on measuring the maximum amount by which the value of solutions to various problems can increase, as a function of the total by which element weights can be increased. We describe an efficient approach for computing this robustness function for any matroid optimization problem. We then concentrate on several specific matroids, such as graphic (minimum spanning tree), transversal (matching in a bipartite graph), scheduling (of unit-time jobs), and partition (resource allocation), for which we can give algorithms more efficient than our general-purpose one. (Joint work with Roberto Solis-Oba.)