This paper investigates the role of Inference to the Best Explanation (IBE) in Explainable Artificial Intelligence (XAI), arguing that IBE can both act as a framework for revealing the considerations and preferences behind XAI explanations and for guiding and evaluating them in a more rigorous manner. The paper focusses specifically on post-hoc explainability and model agnostic techniques, illustrating the argument through examples of salience maps and feature importance techniques. Here, IBE in XAI happens in two steps. The first aims at maximising the range and accuracy of possible inferences made; the second aims to provide a certain balance of explanatory virtues given a certain why-question and stakeholder that requires an explanation. Using the language of explanatory virtues enables a more nuanced discussion about what we may like or dislike about certain explanations in the current XAI landscape and provides actionable ways of improving explanations.