As bridges with stay cables or external post-tensioning tendons near the end of their service life, there is heightened emphasis on evaluating their structural performance (of these vulnerable structural elements) ensuring alignment with modern safety and operational standards. This fact has driven significant research into non-destructive techniques for external tendons, particularly in vibration-based structural health monitoring (SHM). SHM systems attempts to estimate critical performance parameters, including natural frequencies, tension forces, and bending stiffness, from acceleration data from cables measured on the structure. Among these parameters, the tension force is indirectly estimated using natural frequencies, cable length, and linear density and assuming particular boundary conditions through analytical models. Despite its conceptual simplicity, this process faces practical challenges: such as frequency doublets which complicate modal identification, while uncertainties in material properties (e.g., fluctuating linear density) introduce errors in tension estimation. A further critical challenge lies in achieving high-precision, in-line tension estimation considering general boundary conditions which implies an optimization problem which makes this process unfeasible unless using simplified models. One alternative is to train machine learning (ML) models using the tendon dynamic equation. Thus, this work explores the use of ML-based regression models to estimate the tension force in external post-tensioning tendons and cables with non-negligible bending stiffness (grouted tendons) are considered which can be short and have general boundary conditions. Different ML models with varying complexity have been trained to compare their performance based on different error metrics. Finally, the models are tested using real data from a continuous SHM system.