Tamper-respondent assemblies, electronic packages and fabrication methods are provided which incorporate a vent structure. The tamper-respondent assembly includes an electronic enclosure to enclose, at least in part, an electronic component(s) to be protected. The electronic enclosure includes an inner surface, and an air vent. A tamper-respondent electronic circuit structure is provided which includes a tamper-respondent sensor disposed to cover, at least part, the inner surface of the electronic enclosure, and define, at least in part, a secure volume about the electronic component(s). The vent structure includes at least one air passage coupling in fluid communication the secure volume and the air vent of the electronic enclosure to allow air pressure within the secure volume to equalize with air pressure external to the tamper-respondent assembly.