Under the three-day amnesty which began on Saturday, Ukrainians living in villages across the river can traverse the Dnipro during daylight hours and to a designated point.
Anastasiia, who also only gave her first name, said she was at the port because she hoped to cross the river the other way, into Russian-held territory where her relatives are.
Russian forces have intensified artillery attacks on the Kherson region since withdrawing from the western bank of the Dnipro.
Dozens have died in attacks in the region, Ukrainian officials say.
Mykola, 73, said his daughter happened to be on the east bank of the river when Kherson was liberated and got stuck alone in Russian-held territory.