Certifying results by checking proofs and models is an essential feature of modern SAT solving. While incremental solving with assumptions and core extraction is crucial for many applications, support for incremental proof certificates remains lacking. We propose a proof format and corresponding checkers for incremental SAT solving. We further extend it to leverage resolution hints. Experiments on incremental SAT solving for Bounded Model Checking and Satisfiability Modulo Theories demonstrate the feasibility of our approach, further confirming that resolution hints substantially reduce checking time.