Ensuring access to the most relevant knowledge contained in large ontologies has been identified as an important challenge. To this end, minimal modules (sub-ontologies that preserve all entailments over a given vocabulary) and excerpts (certain, small number of axioms that best capture the knowledge regarding the vocabulary by allowing for a degree of semantic loss) have been proposed. In this paper, we introduce the notion of subsumption justification as an extension of justification (a minimal set of axioms needed to preserve a logical consequence) to capture the subsumption knowledge between a term and all other terms in the vocabulary. We present algorithms for computing subsumption justifications based on a simulation notion developed for the problem of deciding the logical difference between ontologies. We show how subsumption justifications can be used to obtain minimal modules and to compute best excerpts by additionally employing a partial Max-SAT solver. This yields two state-of-the-art methods for computing all minimal modules and all best excerpts, which we evaluate over large biomedical ontologies.