This paper describes an investigation into developing certified abstract interpreters from big-step semantics using the Coq proof assistant. We base our approach on Schmidt’s abstract interpretation principles for natural semantics, and use a pretty-big-step (PBS) semantics, a semantic format proposed by Charguéraud. We propose a systematic representation of the PBS format and implement it in Coq. We then show how the semantic rules can be abstracted in a methodical fashion, independently of the chosen abstract domain, to produce a set of abstract inference rules that specify an abstract interpreter. We prove the correctness of the abstract interpreter in Coq once and for all, under the assumption that abstract operations faithfully respect the concrete ones. We finally show how to define correct-by-construction analyses: their correction amounts to proving they belong to the abstract semantics.