A wireless communication system may include an electronic device having a wireless communication module. The wireless communication module may include an antenna radiating element on a first surface, a ground ring surrounding the antenna radiating element on the first surface, and a radio component mounted to a second surface. The wireless communication module may be incorporated into a system package that also includes other components. Encapsulation material may cover the wireless communication module and other components. A shielding material may cover the encapsulation material and be coupled to the ground ring. An opening in the shielding material may be aligned with the antenna radiating element. If desired, the wireless communication system may include external equipment having a wireless communication module communicatively coupled to the wireless communication module to convey firmware testing, debugging, restore, and/or other data.