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The electromagnetic (EM) properties of shielded gyromagnetic spheres are characterized with the aid of an electrodynamic model formulated for the transverse electric (TE) modes of an isotropic sphere, in a similar way as dielectric resonators are commonly analyzed. Broadband characteristics of geometric and energy filling factors are presented. A new measure of the magnetic loss tangent is introduced which is positive despite the intrinsic permeability of the gyromagnetic medium being negative, where existing definitions yield a non-physical negative value. The sample size dependence of those quantities is also assessed. The conclusions from the analysis are applied to investigate and de-embed ferromagnetic linewidth errors which can occur in broadband measurements of magnetic garnet spheres. Magnetic anisotropy fields and the gyromagnetic $g$ -factor are also estimated from the measurement data. Experiments were performed in a two-port subwavelength cavity, covering a frequency range of up to 28 GHz. Additionally, two-port rectangular resonant cavity linewidth measurements at a few modes have been conducted. Good agreement between the two methods is found if the systematic error is accounted for. [ABSTRACT FROM AUTHOR]