Geographical indications (GIs) have become increasingly important in agri‐food markets, especially in Europe. For Swiss cheese imports and exports, we analyze whether GIs are associated with higher trade prices. We find that price premiums can be obtained for both exports and imports. However, this is only the case for cheeses with single name GIs where the whole name is protected (e.g., Gruyère, Roquefort). There is no price premium for cheeses with compound names, consisting of a generic part and a geographical part (e.g., Gouda Holland, Raclette du Valais). As the generic part of the name (here Gouda, Raclette) can be used by competitors from other regions, such GI products may have difficulties in differentiating themselves. We conclude that higher prices in international cheese trade are not a matter of having a GI label or not. Rather, having a compound name seems to offset the benefit of the GI protection.