MaxSAT solvers are increasingly used as back-ends in software engineering tools. Yet their results have lacked automatically checkable certificates of optimality. While SAT solvers emit DRAT proofs of (un)satisfiability, MaxSAT must additionally prove that no lower-cost solution exists. Existing approaches either cover only isolated solving paradigms or re-duce MaxSAT reasoning to heavyweight pseudo-Boolean proofs, yielding impractical verification overhead.We present the first MaxSAT-specific proof-logging framework for core-guided OLL solvers. We formalize native inference rules for cores, cliques, hardenings, totalizer updates, and bound adjustments, and implement both a human-readable logger and a compact binary DAG logger in EvalMaxSAT. Evaluation on the 2024 MaxSAT competition dataset confirm the practicality and scalability of our certification pipeline, paving the way for trustworthy, solver use.