Iron-based shape memory alloys (Fe-SMAs) are currently of high interest for potential smart material applications in civil engineering construction but also other fields that do not require biocompatibility but demand low cost of the SMA. The envisioned civil engineering application examples, for some of which prototypes have already been realized, include connectors in concrete, metal, and timber structures, concrete reinforcement, and isolators/dampers for earthquake-resistant technologies. In this contribution, we first present results regarding the experimental characterization of Fe-SMAs using a versatile miniaturized testing method, specifically the small punch test (SPT). Its main advantages are that it is relatively simple, requires only small amounts of material, and allows testing under well-defined biaxial stress states (triaxiality of approximately 0.6). The difficulty of identifying material parameters with this test and its variants is that it always requires the numerical solution of an inverse problem because the experiment records a structural response rather than a pure constitutive response. To address this, an in-house parameter identification tool has been developed, which combines finite element analysis, user-defined material models, and nonlinear optimization algorithms. Building on this expertise, our current contribution investigates the employment of the SPT as an efficient methodology to characterize Fe-SMAs under biaxial loading. Such data is of great interest to constitutive model developers for both calibration and validation purposes. Generally, sufficiently rich experimental data on SMA behavior that goes beyond results obtained in one-dimensional tests (e.g., tension-compression-torsion or planar-biaxial loading) is scarce in the literature.