value bets with A high?

Is it ever correct to value bet with A high.
Typical example would be SB v BB.
Your BB and SB tries to steal the pot post flop with a min bet.
You have none of it but also think you’re A high is still ahead.
You call the bet and see a turn. Turn pairs the board or puts something there that you don’t think hit SB.
SB checks and you check behind. River is yet another blank. SB checks but you also know SB to pay off small bets just to see what you have. for example SB would call a min bet with K or Q high here.
Is it correct to bet here?
This may sound silly seen as I’ve described the situation as I know im ahead and I know SB will call me with K high so obviously its correct to bet but my question is similar situations where the pot is relatively small and the hand has been played mostly passive post flop with no betting or maybe a min bet on one street .