Changes in runoff from Greenland and Antarctica are often cited as one of the major concerns linked to anthropogenic changes in climate. The changes in mass balance, and associated changes in sea-level, of these two ice sheets are examined by comparing the predictions of the six possible combinations of two climate models and three methods for estimating melting and runoff. All models are solved on 20 and 40 km grids respectively for Greenland and Antarctica. The two temperature based runoff parameterizations give adequate results for Greenland, less so for Antarctica. The energy balance based approach, which relies on an explicit modelling of the temperature and density structure within the snow cover, gives similar results when coupled to either climate model. The Greenland ice sheet, for a reference climate scenario similar to the IPCC's IS92a, is not expected to contribute significantly to changes in the level of the ocean over the 21st century. The changes in mass balance in Antarctica are dominated by the increase in snowfall, leading to a decrease in sea-level of 4 cm by 2100. The range of uncertainty in these predictions is estimated by repeating the calculation with the simpler climate model for seven climate change scenarios. Greenland would increase the level of the oceans by 0 - 2 cm, while Antarctica would decrease it by 2.5 - 6.5 cm. The combined effect of both ice sheets lowers the sea-level by 2.5 - 4.5 cm over the next 100 years, this represents a 25% reduction of the sea-level rise estimated from thermal expansion alone. This surprisingly small range of uncertainty is due to cancellations between the effects of the two ice sheets. For the same reason, the imposition of the Kyoto Protocol has no impact on the prediction of sea-level change due to changes in Greenland and Antarctica, when compared to a reference scenario in which emissions are allowed to grow unconstrained.