  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 metocean
data sets, with diagnostics indicating generally good performance.
