Cyber-physical attacks impose a significant threat to the smart grid, as the cyber attack makes it difficult to identify the actual damage caused by the physical attack. To defend against such attacks, various inference-based solutions have been proposed to estimate the states of grid elements (e.g., transmission lines) from measurements outside the attacked area, out of which a few have provided theoretical conditions for guaranteed accuracy. However, these conditions are usually based on the ground truth states and thus not verifiable in practice. To solve this problem, we develop (i) verifiable conditions that can be tested based on only observable information, and (ii) efficient algorithms for verifying the states of links (i.e., transmission lines) within the attacked area based on these conditions. Our numerical evaluations based on the Polish power grid and IEEE 300-bus system demonstrate that the proposed algorithms are highly successful in verifying the states of truly failed links, and can thus greatly help in prioritizing repairs during the recovery process.