In this work a multi-objective design optimization-under-uncertainty of a U-bend is performed. The objectives of this problem are maximizing the mean heat transfer and minimizing the mean pressure loss and their respective variances for serpentine heat transfer passages. The flow operates near the saturation conditions which leads to phase change. The U-bend was parameterized by means of Bézier curves and the flow in each design was evaluated by means of unsteady Reynolds-averaged Navier-Stokes (URANS) simulations. A description of the histogram of heat transfer and pressure loss constructed from the timeseries of the URANS simulations is fed to the optimizer as a function of the parameterization of the U-bend and a description of the operational uncertainties. Use is made of the efficient robust global optimization (ERGO) methodology, a reformulation of Bayesian optimization to simultaneously minimize mean and variance of the objective, and is motivated by the computational load of the optimization problem. The result shows optimized designs that outperform the standard design in the different metrics. A trade-off between levels of robustness can be observed, as well as between the deterministic optimization criteria. This result allows the designer to select a compromising geometry between the criteria depending on the application type of the U-bend and proves the effectiveness of the design-under-uncertainty approach.