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A methodology to efficiently design novel products based on magneto-dielectric materials containing ferrite or magnetic alloy inclusions is presented. The engineered materials should provide desirable frequency responses to satisfy requirements of electromagnetic compatibility/immunity over RF and microwave bands. The methodology uses an analytical model of a composite magneto-dielectric material with both frequency-dependent permittivity and permeability. The Bruggeman asymmetric rule for effective permeability of a composite is modified to take into account demagnetization factors of inclusions, and is shown to be applicable to platelet magnetic inclusions. Complex permittivity and permeability are extracted from the transmission-line measurements. A novel accurate and efficient curve-fitting procedure has been developed for approximating frequency dependencies of both permittivity and permeability of magneto-dielectric materials by series of Debye-like frequency terms, which is important for wideband full-wave numerical time-domain simulations. Results of numerical simulations for a few structures containing magneto-dielectric sheet materials and their experimental validation are presented.