Catching leakers involves leaving juicy bits of gossip and other interesting material where it can be seen by suspected leakers to see if they take the bait- this means the “most alarming” stories we keep seeing in the press and that frequently turn out to be fake are most likely derived from tempting bait left out by leak hunters that various leakers have bitten on and forwarded to the press.
If you are looking to press charges against said leakers you also need to catch them knowingly leaking what they believe is or what actually is classified material.
The Canary Trap, as popularized by Tom Clancy in Hunt for Patriot Games, one of my most favorite fictional books.