Microwave resonance data at 35 GHz were obtained on single‐crystal spheres of Ba3 Zn 2Fe2 4O4 1 (Zn 2Z) at room temperature. Values derived for the anisotropy field, saturation magnetization and first order anisotropy constants are H a =4.81±0.04 kOe, M 0=316±20 G, and K 1=+0.76±0.05×106 erg/cm3, respectively. The lowest resonance linewidth observed is ΔH=38 kOe. A phenomenological model is developed for predicting values of K 1 for zinc‐containing hexagonal ferrites.