The orthorhombically distorted perovskite NaMnF$_{3}$ has been predicted to become ferroelectric if an $a=c$ distortion of the bulk $Pnma$ structure is imposed. In order to test this prediction, NaMnF$_{3}$ thin films were grown on SrTiO$_{3}$ (100) single crystal substrates via molecular beam epitaxy. The best films were smooth and single phase with four different twin domains. In-plane magnetization measurements revealed the presence of antiferromagnetic ordering with weak ferromagnetism below the Néel temperature $T_N=66$ K. For the dielectric studies, NaMnF$_{3}$ films were grown on a 30 nm SrRuO$_{3}$ (100) layer used as a bottom electrode grown via pulsed laser deposition. The complex permittivity as a function of frequency indicated a strong Debye-like relaxation contribution characterized by a distribution of relaxation times. A power-law divergence of the characteristic relaxation time revealed an order-disorder phase transition at 8 K. The slow relaxation dynamics indicated the formation of super-dipoles (superparaelectric moments) that extend over several unit cells, similar to polar nanoregions of relaxor ferroelectrics. ; Comment: 4 pages, 3 figures