Electromagnetic vortices in a microwave cavity with an inserted piece of a magnetized ferrite appear due to the time-reversal symmetry breaking effect. We reveal numerically that the Poynting-vector vortices are possible in open resonant microwave structures with ferrite inclusions. We demonstrate a pair of resonances which have opposite vortex rotations at the same direction of time given by the direction of the magnetization precession. There are two coalescent resonances with different chirality. We show that the structures of the radiating near and far fields are intimately related to the ferrite-induced topological singularities. The observed far-field polarization structures represent a doublet of chiral vortices in space originated from a doublet of resonant chiral states in a patch resonator with an enclosed ferrite disk.