Mixtures of fluoride molten salts such as LiF + BeF2 (Flibe) and LiF + NaF + KF (Flinak) have been proposed as tritium breeders for fusion reactors and heat-transfer fluids for high-temperature fission reactors. The melting point of mixed molten salts is important in fusion and fission reactor designs. An analytical method using the activity coefficient of the Margules’ equation and another method using an equilibrium constant when a new phase appears in the phase diagram are proposed for calculating melting points according to whether or not the new phase appears. First, the melting points of pure fluorides of LiF, NaF, KF, and BeF2 are investigated in detail, and uncertainties in the thermodynamic properties of the targeted molten salt mixtures are clarified. Then, the melting points of some binary- and tertiary-component fluoride molten salt mixtures of LiF + NaF (Flina), LiF + KF (Flik), NaF + KF (Fnak), LiF + NaF + KF (Flinak), LiF + BeF2 (Flibe), and NaF + BeF2 (Fnabe) are analytically investigated to enhance their wider application in fusion and fission reactors. Estimated melting points are compared with experimental data reported previously. Estimation errors are within 3.0 K (0.3%) for the pure fluorides and within 34 K (5.2%) for the binary or tertiary fluoride mixtures. Although estimation errors for the Flinak system are larger than those of previous reference data, the present estimation does not include an accommodation factor, and the parameter values included in the estimation are consistent with other thermodynamic data. The values of the activity coefficient used for estimation of the Flinak system and the equilibrium constant included in estimation of the Flibe and Fnabe systems are consistent with relevant thermodynamic properties. Therefore, the present method can be applied to estimate melting points for a range of multicomponent fluoride mixtures.