System identification has been a major advancement in the evolution of engineering. As it is by default the first step towards a significant set of adaptive control techniques, it is imperative for engineers to apply it in order to practice control. Given that system identification could be useful in creating a digital twin, this work focuses on the initial stage of the procedure by discussing simplistic system order identification. Through specific numerical examples, this study constitutes an investigation on the most “natural” method for estimating the order from responses in a convenient and seamless way in time-domain. The method itself, originally proposed by Ho and Kalman and utilizing linear algebra, is an intuitive tool retrieving information out of the data themselves. Finally, with the help of the limitations of the methods, the potential future outlook is discussed, under the prism of forming a digital twin.