More recently, Explainable Artificial Intelligence (XAI) research has shifted to focus on a more pragmatic or naturalistic account of understanding, that is, whether the stakeholders understand the explanation. This point is especially important for research on evaluation methods for XAI systems. Thus, another direction where XAI research can benefit significantly from cognitive science and psychology research is ways to measure understanding of users, responses and attitudes. These measures can be used to quantify explanation quality and as feedback to the XAI system to improve the explanations. The current report aims to propose suitable metrics for evaluating XAI systems from the perspective of the cognitive states and processes of stakeholders. We elaborate on 7 dimensions, i.e., goodness, satisfaction, user understanding, curiosity & engagement, trust & reliance, controllability & interactivity, and learning curve & productivity, together with the recommended subjective and objective psychological measures. We then provide more details about how we can use the recommended measures to evaluate a visual classification XAI system according to the recommended cognitive metrics.