No need to worry; there's nothing to fear; everything is under control.
荷物は宅配業者が受け取ってくれたから、あなたは心配無用だ。
The courier has collected the package, so you don't need to worry.
この件は私が対応するので心配無用です。
I'll handle this matter, so there's no need to worry.
天気予報では晴れなので遠足は心配無用だ。
The forecast says it will be sunny, so there's nothing to worry about for the excursion.
機器は自動で停止するから過負荷は心配無用だ。
The machine will stop automatically, so you don't need to worry about overload.