We analyze how concerns for model misspecification on the part of international lenders affect the desirability of issuing state-contingent debt instruments in a standard sovereign default model à la Eaton and Gersovitz (1981). We show that for the commonly used threshold state-contingent bond structure (e.g., the GDP-linked bond issued by Argentina in 2005), the model with robustness generates ambiguity premia in bond spreads that can explain most of what the literature has labeled as novelty premium. While the government would be better off with this bond when facing rational expectations lenders, this additional source of premia leads to welfare losses when facing robust lenders. Finally, we characterize the optimal design of the state-contingent bond and show how it varies with the level of robustness. Our findings rationalize the little use of these instruments in practice and shed light on their optimal design.