A container for containing a perishable substance has a container wall with an inner side and an outer side. The wall has an electrically conductive layer extending between the inner side and the outer side. The inner side faces the space containing the substance. The container comprises electronic circuitry having a sensor for sensing a physical property or condition of the substance, and an antenna for communicating an RF signal to a receiver, external to the container. The RF signal is indicative of the physical property or condition sensed. The sensor is positioned so as to be exposed to the space containing the substance in operational use of the container. The antenna is positioned at the outer side, or between the outer side and the electrically conductive layer, and is electrically isolated from the electrically conductive layer.