We consider longevity risk hedging problems, where survivor swaps are available as hedging instruments. As objective functions we consider the mean-variance and the mean-conditional-value-at-risk of the hedged liabilities, evaluated using an estimated probability law governing the mortality dynamics. To be robust against estimation inaccuracy, we optimize the worst-case value of the objective function, where the worst-case is with respect to a statistical confidence set around the estimated probability law. We derive reformulations of the worst-case optimization problems that can be solved easily. In the empirical analysis, we compare the performance of the worst case (robust) optimizations with the (non-robust) optimizations that ignore the estimation inaccuracy. We find that the robust optimizations perform better when the actual and estimated probability laws deviate, which is likely to happen in the presence of estimation inaccuracy.