Perhaps when Naruto is about to make a very dangerous decision that could cost him his life. Minato's presence, whether it's a memory or an actual spiritual manifestation, stops Naruto in his tracks. Minato's voice echoes in Naruto's mind, warning him and guiding him to a safer path. This shows not only Minato's protectiveness but also his deep connection with his son. Another moment could be when Naruto is being bullied as a child. Minato's residual power within Naruto could flare up, scaring off the bullies and wrapping Naruto in a warm, protective glow. It's a moment that shows Minato's love and protectiveness reaching out even from the past.
One touching moment could be when Minato's spirit appears right in front of Naruto when he is on the verge of being defeated by a powerful enemy. Just seeing his father's figure gives Naruto new strength and hope, which shows Minato's protectiveness in a very emotional way.