<p>Artificial intelligence (AI) is increasingly being used in the cultural heritage (CH) sector to analyse, interpret and conserve artefacts and architectural features. While these technologies offer significant opportunities, concerns have been raised regarding transparency, fairness and interpretability. This paper proposes a methodology for fostering trustworthy AI in the CH sector that embeds explainability and bias-mitigation strategies directly into AI-driven analysis. The methodology integrates contextual insights with multidimensional explainability techniques to make AI decision-making processes more transparent and understandable. A case study based on an existing CH analysis framework shows that incorporating explainability can greatly increase user confidence, promote ethical alignment, and encourage responsible use. The findings emphasise the importance of clarifying AI outputs for heritage professionals, as well as ensuring that AI systems respect cultural specificity and interpretive accuracy.</p>