Mike Mearls stated over Twitter that Intelligence could be used for resisting Psionics, when they get around to it, and Charisma could be used for resisting possession. However, those are both magical uses and don't fit your criteria of saving throws involving these two attributes for resisting non-magical effects.
To my knowledge, there are no official uses of these. However, some situations that a DM may choose to use them include:
Saving throws would focus on using logic, deductive reasoning, memory, and education to avoid unfavorable outcomes.
- Realizing that someone is drawing you into a verbal trap
- "That's a loaded question. Either answer I give you would look badly on me."
- "You're using faulty logic in your argument."
- Knowing that you are being scammed
- "The odds of winning Three Dragon Ante aren't this good, something is up."
- "I'm not paying 50 silver for that bauble, I know you got it for 10!"
- Remembering a piece of information
- "What did he say...oh yeah! I remember now!"
- "I only briefly saw the heraldry, but I think I can remember what it looks like"
Saving throws would focus on influencing others, making an impression, or navigating social situations to avoid an unfavorable outcome
- Recovering from a faux paus in court
- "I didn't bow because I wanted to bow last. See, here I'm bowing now."
- "I had no idea that wearing hats in court is a mistake. Where I come from, it's a badge of respect."
- Correcting a bad first impression
- "Despite what you just saw, we're the good guys!"
- "We started off on the wrong foot. I'm a lot better when you get to know me properly."
- Maintaining a desired expression when internally you don't feel that way
- "No, seeing that person beaten doesn't bother me."
- "I'm fine, that wound doesn't hurt nearly as bad as it looks."