We compare hindcasts of global mean sea level over the past millennium obtained using two semi-empirical models linking temperature and sea-level rise. The models differ in that one of them includes a term for a very long-term sea-level rise component unfolding over many millennia. On short (century) time scales, both models give very similar results. 

Proxy sea-level reconstructions from the northern (North Carolina) and southern (New Zealand and Tasmania) hemispheres are used to test the ability of both models to reproduce the longer-term sea-level evolution. In both comparisons the model including the second term produces a markedly better fit from 1000 AD to the present. 

When both models are used for generating sea-level projections, they behave similarly out to 2100 AD. Further out, to 2300–2500 AD, the projections differ significantly, in no small part due to different values for the sea-level response time scale τ obtained. We conclude that careful model validation on long time scales is important before attempting multi-century projections.