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Developing digital twins for electromagnetic devices often relies on numerical simulation data, as physical experiments can be prohibitively expensive. Consequently, ensuring the reliability of such data is essential. In engineering practice, the primary objective is often not to minimize the global discretization error, but to guarantee high accuracy for specific quantities of interest (QoIs). A posteriori error estimation for QoIs provides a rigorous framework for this validation. However, obtaining reliable error bounds typically requires the construction of an admissible solution. Conventionally, this is achieved by solving a dual problem over the entire computational domain, which incurs a significant computational cost. To mitigate this burden, we propose a local approach for constructing the admissible solution, based on a local flux reconstruction technique. We apply this approach to 3D magnetostatic problems, specifically accounting for discontinuities in material properties within the domain. Numerical results demonstrate that the proposed local approach achieves accuracy comparable to the global approach, offering a promising, computationally efficient alternative for constructing admissible solutions.