This paper explores a model-centred approach to augment the development and refinement of the theory of emergence. Its focus is on the relational process of leadership as an emergent event in complex human organisations. Emergence in complex organisations is a growing field of inquiry with many remaining research opportunities, yet a number of its central themes continue to be loosely connected to practical application and reliant on equivocal translations from root meaning. This paper offers a novel model of semantic conceptualisation of theory and phenomena with simulations to strengthen the theory–model–phenomenon link, building on the work of previous authors. Strengthening this link yields numerous applications, including making sense of complex organisational dynamics and supporting a wide range of theory-building research methods in applied social science and interdisciplinary research. The paper begins with a reflection on the main ideas of the theory of emergence, followed by discussion on prevalent model-centred approaches. A programme of semantic conceptualisation to expand real-world application of the theory of emergence is proposed.