  Let $\k$ be a field, and let $A$ and $B$ be connected $\N$-graded
$\k$-algebras. The algebra $A$ is said to be a graded right-free extension of
$B$ provided there is a surjective graded algebra morphism $\pi: A \to B$ such
that $\ker\pi$ is free as a right $A$-module. Suppose that $B$ is graded left
coherent, and that $A$ is a graded right-free extension of $B$. We characterize
when $A$ is also graded left coherent. We apply our criterion to prove graded
coherence of certain non-Noetherian graded twisted tensor products.
