The seismic assessment of rocking masonry structures is a complex task, due to the high sensitivity of the behavior to the characteristics of the input motion. The paper compares the results offered by different models and the reliability of widely used intensity measures. A displacement-based approach based on an incremental limit analysis of rigid blocks is proposed for the performance-based assessment of rocking masonry structures, such as: rocky structures (archeological remains, obelisks, columns, trilithons), arch-piers systems (e.g. triumphal arches, belfries), out-of-plane mechanisms of walls (standing out walls, facades in buildings or churches etc.) or artistic assets prone to overturn (pinnacles, statues etc.). The method is compatible with the format of the PERPETUATE performance-based assessment method for cultural heritage assets