In general I'm against it because it's extremely difficult to be consistent. Sure, if the PC Paladin's Turn Undead isn't clear, then it's easy enough to say that when the PC Wizard casts charm person success is unclear. However, when a vampire gazes at the Rogue, success should be unclear to the vampire, too. That's not really possible because the DM -- the NPC's player -- is going to know the DC and the result of the save. And what about fireball? Lightning bolt? Harm? Slow? Phantasmal force? You've now got to decide on the visual effects of every spell or effect that grants a save. Your players will ask about skill checks to determine if things work, and now you've just added a ton of dice rolling to spellcasting. Honestly, it's easier just to tell the PCs if things they cast work or not. Restricting it to just the caster is reasonable, but I don't find it to be a significant metagaming problem because both sides can do it.
The only time I've ever really hidden the results of a save it is for dramatic effect, and only for things the players don't have an inherent understanding of.
In one case in 3.5e, the players encountered a very young blue dragon, and it kicked their butts pretty soundly. The PCs could have killed it easily had they gotten into melee, but there was no way the dragon was that stupid. The PCs managed to get away with the help of a scroll and some potions, and then procured a single arrow of blue dragon slaying by petitioning the local church -- and paying a fair bit of gold. The arrow was made from a single piece of black wrought iron, heavily pitted as if it had been left out to rust, and the fletchings were metal combs with teeth like fir needles. They went back, found the dragon, and in the first few rounds of combat used true strike and fired the arrow at the dragon. The arrow hit, pierced the dragon's hide, and I rolled to save. And nothing happened. The just arrow stuck out of the dragons chest. I had them roll normal arrow damage and marked it down. The players all got very nervous. On the dragon's next turn, it tried to breathe it's lightning breath. However, as soon as it inhaled deeply, a bolt of electricity traveled from inside the dragon's chest, down the arrow, and struck the earth. The dragon shrieked in pain as the arrow drew the life energy from the dragon and grounded it like a lightning rod (which, indeed, is what the arrow was created from). Within moments the dragon was dead. The dragon had failed it's saving throw.
I'd already decided when I gave the party the arrow that it the worked by using the power of the dragon against itself, but none of them investigated the arrow. They assumed that it would work like finger of death, but it didn't. The characters had no foreknowledge of how such an arrow might work, except beyond book learning and hearsay (which, in my games, is all the DMG and MM count for). Therefore, it was completely appropriate that the PCs wouldn't have any idea how the item worked and had no idea how to tell if a save had succeeded or failed.