“De rien” might seem a bit flippant for this kind of occasion.

You could use “Il n’y a pas de quoi,” “Il n’y a pas de quoi me remercier,” or come up with something less formulaic that expresses your actual thoughts on the matter. For example, you could say “C’était normal que je le fasse,” “J’étais content de pouvoir le faire,” or something similar.

I think the best answer should be : “Je t’en prie” or “Je vous en prie”.
This is polite and can be used on formal and informal context.