An important direction of fusion research is the reconstruction of plasma equilibrium from measurements. Most of the plasma modeling codes and plasma control systems use equilibrium data on input. Therefore, the accuracy of reconstructions plays a crucial role in fundamental understanding of processes in present-day devices and fusion reactors. The results of previous research show that one can get substantially different reconstructions of plasma current densities and safety factors, which fit the measurements even within a relatively small inaccuracy. So, rigorous calculation of the reconstructed function error bars is required. This paper presents new advances in formulation of the equilibrium reconstruction problem for the epsilon-net (ε-net) framework, describes application of the ε-net technique for rigorous calculation of the reconstruction error bars and its implementation in the European Integrated Modeling (EU-IM) platform, and gives examples of error bar evaluation for ASDEX Upgrade concentrating on the plasma pressure constraint analysis.