What happened to Rin's Mana Compass?
To the best of my knowledge, it's never mentioned again (not even later in Fate/Zero), aside from a throwaway reference on the Fake/states night webpage, which describes it (魔力針) as an item you could find in-game and which has Rin's name engraved on the back of it. 

From an out-of-universe perspective, the obvious reason why we don't know what happened to it is that it was invented by Urobuchi for Fate/Zero, which was written after Fate/stay night, and it's not so important an object that its whereabouts in Fate/stay night would need to be explained. 

From an in-universe perspective, I think the best explanation is that by the time of the Fifth War, Rin no longer needed the device - skilled mages can already sense magic to some extent. During the Fourth War, though, when she was just 5 or 6, she probably wasn't experienced enough to be able to detect mana all that effectively, and so the compass was somewhat useful to her back then.

By the way, 


   Rin doesn't get the pendant during Fate/Zero. It's only at the beginning of F/SN (the day before she summons Archer) that she finds it with her father's effects. Rin does happen to show up at the end of Fate/Zero (for Tokiomi's funeral); that's when she receives the Azoth sword from Kirei.