Despite the professional importance attached to the antenna theory and design course, most students and some academics still see the course as difficult and not easily explained via mathematical modelling (MM) despite some mathematical concepts integrated into the teaching and learning of an antenna theory and design. Due to this challenge, some students change their courses and opt for courses with less mathematical complexity. In view of this, this paper reports the review on the teaching and learning of an antenna theory and design using MM approach, relevant theoretical models reported by other researchers, with a comparative description of these theoretical frameworks. It also offers an empirical appraisal of a practical-realistic pedagogic mathematical model for teaching and learning an antenna theory and design course (PRPMM-TLATD) as a reliable model in the universities. In achieving this, data was gathered from four scholarly academics and 12 engineering students from a university in South Africa using qualitative approach. This finding generates the following stages as reported by the participants. And these stages include antenna validation by measurement, antenna validation by simulation, analysis of an antenna mathematically, personal conceptualization of the design work, total interpretation and validation of design problem, and problem resolution by mathematization. It also confirmed that the teaching and learning the design problem, antenna parameters modelling (mathematically), describing an antenna parameters mathematically, extra-mathematical working and prerequisite courses model were followed. The result of the study confirmed that the teaching and learning of an antenna theory and design could be classified into two domains, namely, paper-based design domain and a realistic domain as gathered from the data among engineering academics and students teaching and learning MM in a university in South Africa.