How to make my xbox trust a self signed certificate?

you can't, Xbox browser is not intended as a cool beat your web browser and has many things disabled to prevent malware

It might be that the Xbox 360 browser doesn't have an up to date root certificate library, and that some pages use a digital certificate that is unknown to the Xbox 360. Or it might be that you are trying to go to a site with a self signed certificate (e.g.
a smart home device in your own network).

There is unfortunately nothing you can do about that, as you can't add anything to the Xbox 360's certificate storage.

Depending on what page you are surfing to, you could try to visit the page via unencrypted http instead of https, or if you REALLY trust the page and don't have to transmit personal information like credit card data or passwords, you can ignore the warning.

Instead of creating a "sniffable" environment that undermines the security of encrypted traffic for the sake of age appropriate content, I'd rather recommend using the whitelist feature of allowing only certain websites for your kid, or only allow certain
age appropriate software.

I don't know what exactly you try to achieve by sniffing SSL traffic, but if kids find out their parents "sniffing" around their (valid personal) secrets, this will eventually lead to your kids not trusting you.

And in extreme situations, they might then seek trust in people other than their parents, through non-digital means, that you can't control.

So talk to your kids and explain them what you think is age appropriate for them and explain why you want to keep them away from some content.

Making kids understand why some adult material is bad, keeps them away from that content by themselves, if they trust your reasons, why you want to protect them from those things. At least in my experience

There's a lot going on here skipping a few key things in order to progress with what you're asking. Do you have access to the firewall and its configuration? What led you to the conclusion that you need to install a Root Certificate Authority for it to
function through the firewall?

The firewall inspects traffic that comes in and goes out of a network. It's acting as a boundary guard between a local network and the world wide web (I could have just said the internet, but I'm going full training video here). As a boundary guard, if
you have access to the configuration, it will do what you tell it to do, and no more. So if you have access to the configuration, you can configure it to allow

all Xbox Live ports through the firewall, either for the entire network or limit it down to the one specific device.

So if you could provide a bit more information about how you got from point A to point

Root Cert issued by a Root Certificate Authority is needed, that can help us solve the trouble you're having, which I'm assuming is your Xbox Live network traffic isn't getting out to the internet, correct?

+1

I would like to inspect encrypted traffic to ensure it is age appropriate.