We calculate the $\omega \to {\pi }^0{\gamma }^{*}$ and $\varphi \to {\pi }^0{\gamma }^{*}$ electromagnetic transition form factors based on dispersion theory, relying solely on a previous dispersive analysis of the corresponding three-pion decays and the pion vector form factor. We compare our findings to recent measurements of the $\omega \to {\pi }^0{\mu }^{+}{\mu }^{-}$ decay spectrum by the NA60 collaboration, and strongly encourage experimental investigation of the Okubo-Zweig-Iizuka forbidden $\varphi \to {\pi }^0{\ell }^{+}{\ell }^{-}$ decays in order to understand the strong deviations from vector-meson dominance found in these transition form factors.