Interval methods can provide guaranteed solutions to difficult nonlinear problems, such as the global optimization of non-convex criteria or the characterization of sets defined by nonlinear inequalities. They can even deal with problems involving quantifiers, as encountered for example in robust control design. For high dimensional problems; their efficiency can be considerably improved by resorting to constraint propagation. In this paper, key ideas of interval analysis and constraint propagation are presented and applied to two problems. The first one is the guaranteed characterization of the set of all parameter vectors that are consistent with experimental dat up to bounds on the acceptable errors. The second one is the design of a PI controller robustly stabilizing a set of models that may have been obtained as the solution to the first problem.