A textured dielectric panel (305, 520, 625, 745, 925, 1035, 1205) is fabricated by applying a first mask pattern (310, 510, 610, 710, 915, 1015, 1210) to a first side of a solid panel made of a first material that is a ceramic dielectric and then sandblasting the solid panel through the first mask pattern from the first side to at least partially generate a shaped cavity (315, 920, 1040). The shaped cavity of the solid panel may be filled with a-second material (330, 740). The first and second materials have substantially differing dielectric constants. The first side and second side of the solid panel may be metallized (325), forming a patch antenna. The shaped cavities can be made more complex by using additional masking and/or sandblasting steps.