This dataset contains data related to the paper titled "Comparing zero-parameter theories for the WCA and harmonic-repulsive melting lines" by Jeppe C. Dyre and Ulf R. Pedersen, with the abstract: The melting line of the Weeks-Chandler-Andersen (WCA) system was recently determined accurately and compared to the predictions of four analytical hard-sphere approximations [Attia \textit{et al.}, J. Chem. Phys. \textbf{157}, 034502 (2022)]. Here, we study an alternative zero-parameter prediction based on the isomorph theory, the input of which relate to properties at a single reference state point on the melting line. The two central assumptions made are that the harmonic-repulsive potential approximates the WCA potential and that pair collisions are uncorrelated. The new approach gives excellent predictions at high temperatures, while the hard-sphere-theory based predictions are better at lower temperatures. Supplementing the WCA investigation, the face-centered-crystal to fluid coexistence line is determined for a system of harmonic-repulsive particles and compared to the zero-parameter theories. The results indicate that the excellent isomorph-theory predictions for the WCA potential at higher temperatures may be partly due to a cancellation of errors between the two above-mentioned assumptions.