  Recent observations have suggested that there is water ice present on the
surfaces of 24 Themis and 1 Ceres. We present upper limits on the H$_2$O
production rate on these bodies derived using a search for [OI]6300 Angstrom
emission. For Themis, the water production is less than 4.5 $\times$ 10$^{27}$
mol s$^{-1}$, while for Ceres our derived upper limit is 4.6 $\times$ 10$^{28}$
mol s$^{-1}$. The derived limits imply a very low fraction of the surface area
of each asteroid is active ($<$ 2 $\times$ 10$^{-4}$), though this estimate
varies by as much as an order of magnitude depending on thermal properties of
the surface. This is much lower than seen for comets, which have active areas
of 10$^{-2}$ - 10$^{-1}$. We discuss possible implications for our findings on
the nature of water ice on Themis and Ceres.
