With the increasing complexity of applications and user needs, recent research has shifted from a data-information level to a human semantic level interaction. Research has begun to address the increasing use and development of ontologies in various applications, strongly motivated by the semantic web initiative. However, existing conceptual models are not rich enough to incorporate ontologies in one single conceptual schema. To improve this situation, it is necessary to refine modelling formalisms and make them more expressive while ensuring they remain semantically sound. We argue that conceptual modelling methodologies would be semantically richer if they were able to express the semantics of a domain that arises in concrete application scenarios. This paper investigates the incorporation of ontologies into three popular conceptual modelling methodologies, presenting the Ontological Entity-Relationship (OntoER) model, Ontological Object Role Modelling (OntoORM) and the Ontological Unified Modelling Language (OntoUML) class diagram. An extended conceptual framework for modelling ontologies and a transformation algorithm for mapping ontological constructs to relational schemata are provided so that querying the database through the conceptualisation of the database can be managed.