This is a small-scale qualitative case study exploring the importance of employability skills in fresh graduates, as perceived by faculty members and employers. Past studies on employability have primarily used quantitative research methods. This study used concept mapping along with semi-structured interviews to elicit rich data on participants’ perceptions. The author did not find any instance of concept mapping being used for employability research, prior to this study, especially in literature from the United Arab Emirates, where this study was set. Five faculty members and five employers were selected for voluntary participation. They were guided by the researcher into developing visual conceptions of their thought processes related to what they considered key employability skills in fresh graduates and the reasons behind the importance of these skills. The maps were then developed into detailed narratives, before a thematic analysis was conducted to reveal key themes within and across the two participant groups. The research methods used in this study were found to be engaging and meaningful for participants, and offer a novel way of eliciting participant responses in a variety of research areas and topics. The case discusses issues of validity, reliability, and generalizability in qualitative research and the importance of designing focused research questions and adhering to necessary ethical principles, and explains the challenges of concept mapping in qualitative research.