Pathfinder makes it very clear that
Succeeding on a Saving Throw: A creature that successfully saves against a spell that has no obvious physical effects feels a hostile force or a tingle, but cannot deduce the exact nature of the attack. Likewise, if a creature's saving throw succeeds against a targeted spell, you sense that the spell has failed. You do not sense when creatures succeed on saves against effect and area spells.
Is this the same for D&D 5th Edition? In the PHB, no such statement is made.
Situations that come to mind:
- Someone uses Suggestion to suggest a course of action. Can they tell whether or not the target actually resisted its save unless they watch them fulfill the suggestion (or not)?
- Someone casts Cone of Cold. Can they tell the difference between the monsters resisting cold, the monsters making their save, or both applying?