This is totally not official or supported by Brave Search, as far as I can tell, but you can create a search.brave.com DNS zone on your local DNS server and then create either a CNAME record to safesearch.brave.com, or create A records for the IP addresses that safesearch.brave.com currently resolves to.

Eg:

local zone search.brave.com
_  CNAME safesearch.brave.com

or:

local zone search.brave.com
_ A 108.138.246.75
_ A 108.138.246.114
_ A 108.138.246.94
_ A 108.138.246.5

To get Image Search working properly, add an A record to your zone for imgs.search.brave.com that resolves to whatever imgs.search.brave.com actually resolves to. Currently, this is:

$ host imgs.search.brave.com
imgs.search.brave.com has address 108.138.246.79
imgs.search.brave.com has address 108.138.246.113
imgs.search.brave.com has address 108.138.246.66
imgs.search.brave.com has address 108.138.246.18

This is what your local zone should look like on a Windows DNS server:

Windows DNS Local Zone Screenshot

So far, this hack seems to work for our school district in testing.

Updates

  • 2022-06-28 - It looks like Brave Search keeps changing things behind the scenes. As of right now, you also need to add the following A records to your custom zone:
cdn.search.brave.com has address 108.138.246.43
cdn.search.brave.com has address 108.138.246.96
cdn.search.brave.com has address 108.138.246.113
cdn.search.brave.com has address 108.138.246.7