Understanding extreme ocean environments and their interaction with fixed and floating structures is critical for offshore and coastal design. Design contours are useful to describe the joint behavior of environmental, structural loading, and response variables. We compare different forms of design contours, using theory and simulation, and present a new method for joint estimation of contours of constant exceedance probability for a general set of variables. The method is based on a conditional extremes model from the statistics literature, motivated by asymptotic considerations. We simulate under the conditional extremes model to estimate contours of constant exceedance probability. We also use the estimated conditional extremes model to estimate other forms of design contours, including those based on the first-order reliability method (FORM), without needing to specify the functional forms of conditional dependence between variables. We demonstrate the application of new method in estimation of contours of constant exceedance probability using measured and hindcast data from the Northern North Sea, the Gulf of Mexico, and the North West Shelf of Australia, and quantify their uncertainties using a bootstrap analysis.