A microwave transmission arrangement, comprising: an electrically conductive hollow waveguide configured to guide microwave signals in a predefined wavelength range in a predefined propagation mode along a signal propagation path defined by the hollow waveguide, the hollow waveguide having a first waveguide portion with a first waveguide cross-section area, a second waveguide portion between the first waveguide portion and a first end of the hollow waveguide, the second waveguide portion having a second waveguide cross-section area greater than the first waveguide cross-section area, and a conductive transition surface of the hollow waveguide forming a transition between the first waveguide portion and the second waveguide portion; and a microwave circuit board including a dielectric carrier, and a first conductor pattern on a first side of the dielectric carrier, the first conductor pattern including a patch for radiating or receiving microwave signals in the predefined wavelength range, and a first ground plane surrounding the patch, wherein the microwave circuit board has a second conductor pattern on a second side of the dielectric carrier, opposite the first side, the second conductor pattern including a second ground plane arranged opposite the patch and the first ground plane, wherein the first ground plane and the second ground plane are interconnected by electrically conducting vias extending through the dielectric carrier, wherein the first ground plane of the microwave circuit board is in conductive contact with the first end of the hollow waveguide, and extends into the second waveguide portion cross-section area so that the first ground plane is present within an area of the first side of the microwave circuit board that is circumscribed by the hollow waveguide at the first end of the hollow waveguide to define at least one conductive pocket (55a-b) together with a conductive side wall of the second waveguide portion and the transition surface of the hollow waveguide. an electrically conductive hollow waveguide configured to guide microwave signals in a predefined wavelength range in a predefined propagation mode along a signal propagation path defined by the hollow waveguide, the hollow waveguide having a first waveguide portion with a first waveguide cross-section area, a second waveguide portion between the first waveguide portion and a first end of the hollow waveguide, the second waveguide portion having a second waveguide cross-section area greater than the first waveguide cross-section area, and a conductive transition surface of the hollow waveguide forming a transition between the first waveguide portion and the second waveguide portion; and a microwave circuit board including a dielectric carrier, and a first conductor pattern on a first side of the dielectric carrier, the first conductor pattern including a patch for radiating or receiving microwave signals in the predefined wavelength range, and a first ground plane surrounding the patch, wherein the microwave circuit board has a second conductor pattern on a second side of the dielectric carrier, opposite the first side, the second conductor pattern including a second ground plane arranged opposite the patch and the first ground plane, wherein the first ground plane and the second ground plane are interconnected by electrically conducting vias extending through the dielectric carrier, wherein the first ground plane of the microwave circuit board is in conductive contact with the first end of the hollow waveguide, and extends into the second waveguide portion cross-section area so that the first ground plane is present within an area of the first side of the microwave circuit board that is circumscribed by the hollow waveguide at the first end of the hollow waveguide to define at least one conductive pocket (55a-b) together with a conductive side wall of the second waveguide portion and the transition surface of the hollow waveguide.