PASSED BALLS
It is certain that no matter how good a catcher is, balls will get past them. You can call them wild pitches or passed balls, but it doesn't make any difference at the time of the play. The important thing is making sure that the catcher knows how to make the play correctly and how to minimize the damage if there is a runner on third base trying to score. Catchers should always turn to their glove side after they stand up and head back to the ball. This guarantees that the catcher will approach the ball on the side of their body that allows them to already be pointed back towards the field.
As the catcher gets close to the ball, they should slide on their knees and slide to the ball. There is a difference between sliding "to" and "at" that ball. If the catcher slides at the ball, the ball will likely end up underneath their body and make it harder to retrieve to make a throw. By sliding to it, the catcher should end up with the ball out in front of the middle of their body.
The catcher will be in a better position to make a throw to the plate or a base, and this technique permits them to attack more aggressively, especially if the ball is up against the backstop. It also lets the catcher approach the ball without slowing up as they near the backstop, which saves valuable time.
As the catcher gets to the ball, they should rake it into their throwing hand with their glove and NOT try to grab it with the glove to pick it up off the ground. As the catcher rakes the ball into their throwing hand, and as the hands are pulled up off the ground to the middle of the chest, the catcher should also bring the front leg up so that their front foot is flat to the ground with the thigh parallel to the ground. The leg coming up stabilizes the rest of the body as we make the throw back towards home plate.
The catcher should make a firm throw to the pitcher's glove using a velocity appropriate for the distance. Keep in mind that many of these throws will be from about twenty feet away or less. A catcher who makes that throw at even 30 MPH is not giving their pitcher a lot of time to see and catch the ball. In fact, at that distance and release velocity, the pitcher will have about the same reaction time as a hitter does to a 90 MPH fastball in the game of baseball or a 60 MPH fastball in the game of softball. Knowing how little time the pitcher actually has to see and catch the ball, it is important that the catcher throws to the pitcher's glove no matter what. Even if the pitcher has their glove too high to make the tag, the throw should still be made to their glove.
Too often, I see catchers making the hard throw to a location where the tag should be made, but because of the speed, there is little to no chance that the pitcher can react in time to make the adjustment and catch the ball. The ball just sails past the pitcher's knees. It is far better to hit a chest-high glove and miss the tag than let an errant ball get by the pitcher and potentially give another runner an opportunity to move up even further. Practice between catchers and pitchers, with both getting into the proper position, will greatly reduce errors and increase tags at home on passed balls and wild pitches.
In the game of softball, the backstops are a lot closer, so a full approach and throw may not be possible or advisable. Even in the game of baseball, it is possible to be playing on a field without a deep backstop, or the ball could bounce off the backstop and come back to the catcher. In all of these cases, the catcher simply needs to turn in the direction of the ball (not necessarily glove side) and shovel pass the ball back to the pitcher, who should be covering home plate.
PRE-GAME ROUTINE:
Catchers should have a pre-game routine, especially on away games. They should practice sliding in a few locations behind the plate and up against the backstop. They should walk along the grass or dirt line along the backstop, looking for debris or things like sprinkler heads. They should search for anything that will interfere with their gameplay. This also means looking at the bottom of the fence for holes and poorly maintained fencing that may pose a danger to them. Catchers should also get into the habit of throwing a few balls at the backstop before the game to understand how the ball is going to act after it hits it. All of these things will affect our approach to the ball and our ability to make the play. A few moments spent in pre-game assessing the territory (sliding around, examining, checking how the ball will bounce off the backstop) will make a big difference during the game.
FINAL THOUGHTS - PASSED BALLS:
While the goal is to do whatever we can to avoid ever being faced with a ball that gets by us with a runner on 3B, the reality is that it will happen at some point or another. All we can do is make sure that we are prepared to act in that moment and give our team the best chance of getting the out at home plate. At the very least, we want to make sure that our approach doesn't make a difficult situation even worse by making an unwanted error. Act quickly, stay under control, make an accurate throw, and hope for the best.