A searcher explores alternatives sequentially and is unaware of the distribution of values of unexplored alternatives. We are interested in decision rules that perform close to Bayesian optimal ones under any prior, at each point of time, and after each history of observations. We call such rules dynamically robust. Standard rules used in the search literature are based on cutoff strategies and are not dynamically robust. We uncover general principles that make this rich setting tractable. We derive a dynamically robust decision rule, which involves randomized behavior and can be approximated by a rule with a linear stopping probability.