Seriously, in some hunting situations there is no solution. Unlike a range, hunting isn't set up to insure a backstop to see your splash. Hence why hunting shots are typically taken at much shorter distances than what we engage steel targets; there generally isn't a guarantee of a second shot. (Though shooting suppressed does give you a bit of insurance in that regard.)
The only other thing I can mention is using your hearing (I wear my electronic ear pro when hunting). It's kind of hard not hearing that loud slap as a bullet impacts living tissue. The lack of that sound is usually a good indicator you missed.
With deer, you can also judge the reaction of the animal. Does it ball up and kick? Does it jump up and kick? Does it just stand there and start getting wobbly? Does it lay down and put it's head on the ground (a good indicator that the lung cavity is filling with blood)? If you missed, do the deer turn and look where they hear the bullet impact?
For coyotes, you'll sometimes see them reach back and snap at where the round hit, as if they're going after whatever "stung" them instinctively.
Just some random thoughts from what I have seen. I'm sure there are others here who have hunted a lot more than I, and could also offer some insights...