An electronic device may have a housing in which an antenna and a proximity sensor formed from flex circuit structures are mounted. The flex circuit structures may include first and second flex circuit layers. The first and second flex circuit layers may include metal antenna structures and metal proximity sensor electrode structures. Solder may be used to attach electrical components to the flex circuit layers and may be used to electrically connect metal structures on the first and second flex circuit layers to each other. The first and second flex circuit layers may be laminated together using a compressive fixture. The compressive fixture may have a first fixture with a convex surface and a second fixture with a concave surface so that the laminated flex circuit layers are provided with a bend.