In the multivariate setting, estimates of extremal risk measures are important in many contexts, such as environmental planning and structural engineering. In this paper, we propose new estimation methods for extremal bivariate return curves, a risk measure that is the natural bivariate extension to a return level. Unlike several existing techniques, our estimates are based on bivariate extreme value models that can capture both key forms of extremal dependence. We devise tools for validating return curve estimates, as well as representing their uncertainty, and compare a selection of curve estimation techniques through simulation studies. We apply the methodology to two met-ocean data sets, with diagnostics indicating
generally good performance.