Might leans slightly less certain, though many readers hear no difference.
Unsure? Might fits: I might be late tonight.
Formal note? Might again: We might suggest an alternative date.
I could call instead if you prefer. A polite offer, not a maybe; might shifts it.
Paired examples
Suggesting an option? Both work: We could move the call to Friday. We might move the call to Friday. The could version sounds like a friendly proposal on the table; the might version sounds more like you are still weighing it yourself.
Polite request? Stick with could: Could you send the draft by noon? Swapping in might (Might you send the draft by noon?) sounds stilted in a normal work message, so here the choice is real, not a coin flip.
Conditional about your own next step? I could join the call if it helps. I might join the call if it's still going. The could version says the option is open; the might version says you are undecided. Pick the one that matches your actual state of mind, since readers will hear both as acceptable.
Where the choice actually matters
One spot where the two are not interchangeable: past ability. If you mean you were able to do something, only could works. When I lived there, I could walk to work. Saying I might walk to work there changes the meaning to a maybe, and readers will hear that shift.
Watch the trap when possibility and ability sit close together. I could have missed the email can mean it was possible you missed it, or that you were able to miss it and didn't. If you want the maybe reading, might have missed removes the ambiguity.
One caveat that can flip the decision: if your past sentence could be heard either way, rewrite it. The ambiguity is the problem, not either word on its own.