A great variety of new and artificial materials have been created during the last decades, such as metamaterials, various composites and many others. To analyze and determine the characteristics of such materials advanced mathematical methods are applied. This work is devoted to the developing the technique for reconstruction of electromagnetic parameters of multi-sectional anisotropic diaphragms in a waveguide of rectangular cross section. To solve this inverse problem we make use of the method of rotation applied for anisotropic materials and reconstruct the quantities to be determined, including the diaphragm positions, from the values of the transmission coefficient measured at different frequencies. The efficiency and accuracy of computations are validated in the course of analytical-numerical solution to the inverse problem. The developed techniques and obtained results can be implemented in practical measurements when anisotropic materials and media with unknown properties are investigated with the aid of commonly used waveguide devices and analyzers.