In the simplest case, just having it marked as an ELINT ship when you have it on sensors, the justification being that it has some strange emissions that are only needed when using spy equipment. Then the other nations can be appropriately outraged and demand that ship be taken out of service/shoot it down themselves.
Another approach is a more passive notification, say whenever 100 intel points have been gathered on you through ELINT, the being-spied-on empire gets a notification that it's colony is being observed, or that a ship has consistently strange sensor echoes, meaning it's under ELINT observation. In this case I think it'd still be necessary to reveal which ship is doing the spying, assuming you have it on sensors.