Home is where the Heart is.
A Heart, in In Nomine terms, is a crystaline object that is linked to a particular celestial and kept in Heaven or Hell, as appropriate. The Heart will glow when the celestial is in its home realm (Heaven for angels, Hell for demons) and at other times can be used to find where the celestial is. It cannot be removed from the celestial realm and is usually kept under the watchful eye of the celestial's Superior.
An angel or demon who returns to their celestial home without using a Tether will always appear near their Heart.
In Hell, a demon about to go Renegade can try to break their own Heart (if they can get close to it!) to keep their ex-boss from finding them. A Renegade who doesn't manage to do this and later redeems will have their Heart shatter at the moment of Redemption.
In all cases but Redemption (where the demon is being completely transformed), a broken Heart inflicts 3 levels of Discord on the celestial.
Free Lilim who have pledged to no Demon Prince but instead are paying back the favors of Lilith do not get a Heart. This makes it easier for them to run (to the consternation of Asmodeus), but it also means they can't get back to Hell without a Tether.