Methods of fabricating tamper-respondent electronic circuit structures and electronic assembly packages are provided which include, at least in part, a tamper-respondent sensor including one or more formed flexible layers of, for instance, a dielectric material, having opposite first and second sides, and circuit lines defining at least one resistive network. The circuit lines are disposed on at least one of the first side or the second side of the formed flexible layer(s). The formed flexible layer(s) with the circuit lines includes curvatures, and the circuit lines overlie, at least in part, the curvatures of the formed flexible layer(s). In certain embodiments, the formed flexible layer(s) may be one or more corrugated layers or one or more flattened, folded layers.