Abstract: Learning dynamical systems from data has emerged as a pivotal area of research, bridging the realms of mathematics, engineering, and data science. Dynamical systems, which describe how states evolve over time based on underlying mathematical relations, are fundamental for understanding a wide range of time-dependent phenomena. For the use of these systems in practical applications including the design of digital twins, high modeling accuracy as well as interpretability and explainability are essential. All of these desired properties are strongly tied to the internal mathematical structure of the dynamical systems. For example, in the modeling of mechanical or electro-mechanical processes, typically systems with second-order time derivatives occur. In this case, data are usually given in the frequency domain as samples of the corresponding transfer function. To learn such structured systems from frequency domain data, we develop in this work a data-driven second-order balanced truncation approach. This method allows the construction of low-dimensional second-order systems with generalized proportional damping structure by assembling appropriate Loewner-like matrices. Numerical examples demonstrate the effectiveness of the proposed method.