We discuss the problem of the limiting height of quiescent prominences and the relationship of this value to the photospheric magnetic field characteristics. Solar prominences are considered preeruptive states of coronal mass ejections (CMEs). We note that in a model of inverse-polarity filament, the equilibrium is stable only in the region where the photospheric magnetic field falls off with a height not faster than h-1. Current-free magnetic field calculations are compared with the observed prominence heights. It is shown that the maximum stable height of a prominence depends on the vertical gradient value and never exceeds the level where the power is equal to unity in the power-law decrease of the magnetic field. This is a new way to predict prominence eruptions and CMEs. ¿ 2001 American Geophysical Union