Learning dynamical systems from data has become a vital interdisciplinary research area, uniting concepts from mathematics, engineering, and data science. These systems, which describe how states evolve over time according to underlying mathematical laws, are essential for modeling a wide array of time-dependent phenomena. For practical applications, achieving high accuracy, interpretability, and explainability are crucial properties that are inherently connected to the mathematical structure of the dynamical systems. For instance, in modeling mechanical or electro-mechanical processes, systems with second-order time derivatives typically arise, with data available in the frequency domain as samples of transfer functions. To effectively learn such structured systems from frequency domain data, we introduce a data-driven second-order balanced truncation method. This approach enables the construction of low-dimensional second-order models with generalized proportional damping by assembling appropriate Loewner-like matrices. Numerical experiments illustrate the effectiveness and potential of the proposed methodology.