Let $R$ be a noetherian connected graded algebra, generated in degree 1, over an algebraically closed field $k$. A point module is a cyclic $R-module$ with Hilbert series $1/(1-t)$. If $R$ is strongly noetherian --- that is, $R$ remains noetherian upon base extension --- then point modules over $R$ are parameterized by a projective scheme $X$, and this induces a canonical map from $R$ to a twisted homogeneous coordinate ring on $X$. This technique has been very important in ring theory; for example, it was crucial to Artin and Schelter's analysis of noncommutative CP2's (regular algebras of dimension 3). We study an important non-strongly noetherian case, when $R$ is a naive blowup algebra. These are subalgebras of twisted homogeneous coordinate rings on some projective $X$, constructed as noncommutative Rees rings. In this case, the point modules are not parameterized by any projective scheme. We show that the scheme $X$ is a coarse moduli space for point modules up to a certain equivalence relation, and that this moduli space construction recovers the map from $R$ to the twisted homogeneous coordinate ring. This is joint work with Tom Nevins.