  We say that a compact invariant set $\Lambda$ of a $C^1$-vector field $X$ on
a compact boundaryless Riemannian manifold $M$ is robustly shadowable if it is
locally maximal with respect to a neighborhood $U$ of $\Lambda$, and there
exists a $C^1$-neigborhood $\mathcal{U}$ of $X$ such that for any $Y \in
\mathcal{U}$, the continuation $\Lambda_Y$ of $\Lambda$ for $Y$ and $U$ is
shadowable for $Y_t$. In this paper, we prove that any chain transitive set of
a $C^1$-vector field on $M$ is hyperbolic if and only if it is robustly
shadowable.
