I just got back from seeing my father off at the airport.
Literal
Father [object-を] see-off [purpose-に] airport [to-へ] went-came [just now-ところだ].
~たところだ marks a just-completed action. 見送りに行く uses the purpose-of-motion pattern (masu-stem + に + motion verb). 行ってきた combines going with coming back — 'went and returned.'