Continuum robots are a type of robotic device that are characterized by their flexibility and dexterity, thus making them ideal for an active endoscope. Instead of articulated joints they have flexible backbones that can be manipulated remotely, usually through tendons secured onto structures attached to the backbone. This structure makes them lightweight and ideal to be miniaturized for endoscopic applications. However, their flexibility poses technical challenges in the modeling and control of these devices, especially when closed-loop control is needed, as is the case in medical applications. There are two main approaches in the modeling of continuum robots, the first is to theoretically model the behavior of the backbone and the interaction with the tendons, while the second is to collect experimental observations and retrospectively apply a model that can approximate their apparent behavior. Both approaches are affected by the complexity of continuum robots through either model accuracy/computational time (theoretical method) or missing complex system interactions and lacking expandability (experimental method). In this work, theoretical and experimental descriptions of an endoscopic continuum robot are merged. A simplified yet representative mathematical model of a continuum robot is developed, in which the backbone model is based on Cosserat rod theory and is coupled to the tendon tensions. A robust numerical technique is formulated that has low computational costs. A bespoke experimental facility with precise automated motion of the backbone via the precise control of tendon tension, leads to a robust and detailed description of the system behavior provided through a contactless sensor. The resulting facility achieves a real-world mean positioning error of 3.95% of the backbone length for the examined range of tendon tensions which performs favourably to existing approaches. Moreover, it incorporates hysteresis behavior that could not be predicted by the theoretical modeling alone, reinforcing the benefits of the hybrid approach. The proposed workflow is theoretically grounded and experimentally validated allowing precise prediction of the continuum robot behavior, adhering to realistic observations. Based on this accurate estimation and the fact it is geometrically agnostic enables the proposed model to be scaled for various robotic endoscopes.