  A cardinal $\lambda$ satisfies a property P robustly if, whenever
$\mathbb{Q}$ is a forcing poset and $|\mathbb{Q}|^+ < \lambda$, $\lambda$
satisfies P in $V^{\mathbb{Q}}$. We study the extent to which certain
reflection properties of large cardinals can be satisfied robustly by small
cardinals. We focus in particular on stationary reflection and the tree
property, both of which can consistently hold but fail to be robust at small
cardinals. We introduce natural strengthenings of these principles which are
always robust and which hold at sufficiently large cardinals, consider the
extent to which these strengthenings are in fact stronger than the original
principles, and investigate the possibility of these strengthenings holding at
small cardinals, particularly at successors of singular cardinals.
