New methods for identifying the material properties of planar objects as a result of measurements by the eddy current method are proposed. The methods are based on the latest surrogate strategies and advanced optimization techniques that improve efficiency and reduce resource consumption of problem solutions, and balance computational complexity with the accuracy of the results. High-performance metamodels for global surrogate optimization are based on deep truly meaningful fully connected neural networks, serving as an additional function of accumulating apriori information about objects. High accuracy of the approximation of the multidimensional response surface, which is determined by the “exact” electrodynamic model of the testing process, is ensured by performing calculations according to the computer design of a homogeneous experiment with a low weighted symmetric centered discrepancy. The results of numerical experiments performed for full and reduced dimensional search spaces, which can be obtained by linear transformations using the principal component method, are presented. The verification of the methods proved their sufficiently high accuracy and computational performance.