Antenna arrangement for a fill-level measuring device for ascertaining and monitoring a fill level of a medium in a container by means of a microwave, travel-time measurement method, comprising a horn antenna having a horn shaped component for focusing microwaves and a microwave transmissive, process isolating element, which is provided in the region of the exit opening of the horn shaped component facing the medium and which isolates the interior of the horn shaped component from the interior of the container. There is provided for additional focusing of the microwaves a lengthening component, which lengthens the horn shaped component in the radiated direction of the microwaves. The process isolating element is embodied and arranged in such a manner that it isolates the horn shaped component and the lengthening component galvanically from one another.