A new, isoplethic method is used to determine critical lines of azeotropic binary fluid mixtures using vapor-liquid equilibrium data including saturated vapor and liquid densities below the lowest critical temperature of the pure components. Thermodynamic paths that access mixture critical lines from this region of the vapor-liquid surface are described by the liquid volume fraction (set at 1/2), fixed overall composition, and pressure. Data along these paths behave like those for a pure fluid and are extrapolated to the critical line by means of simple, pure-fluidlike expressions for the density difference, vapor pressure, and rectilinear diameter for vapor and liquid in equilibrium. The method is tested successfully for an azeotropic mixture for which critical-point estimates can be compared to those in the literature [C3H8 (propane) + C4F8 (perfluorocyclobutane)]. The method is then applied to the two azeotropic mixtures, R32 [CH2F2 (diflouromethane)] + C3H8 (propane) and R125 [C2F5H (pentaflouroethane)] + C3H8 (propane), for which no information is available on the critical line. Analytical expressions for the critical temperature, critical pressure, and critical density are given as functions of the overall composition for these mixtures. The combination of relatively easily measured vapor-liquid equilibrium data along with a simple, thermodynamically correct path to the critical line provides an efficient, relatively simple method for characterizing the vapor-liquid coexistence surfaces for binary mixtures.