A new method is proposed for accurately measuring the densities of high-temperature liquids which involves analyzing the surface oscillations of levitated droplets. This method makes it easy to improve on the accuracy of density measurements obtained by using conventional electromagnetic levitation systems. In addition, the errors in density measurements made on the ground are further reduced by applying a static magnetic field to suppress surface oscillations in levitated liquid droplets. The magnetic field interacts with electrical currents in the levitated droplet, thereby generating a Lorentz force; this force suppresses flow within the liquid droplet. By combining both these methods, the scatter in density measurements for molten Si at temperatures in the range from 1,500 K to 1,900 K is reduced by an order of magnitude compared with previously reported data. Using this new method, the density of molten SiGe has been measured at temperatures from 1,350 K to 1,650 K.