When the cheese is in the "curd state" I'll take a small wad of curd, squeeze out any whey and wad it up around the flat end of my Extech pH meter. Usually, I'll wiggle it around a bit as the meter is stabilizing. Although it is not good manufacturing practice I usually shred the curd wad and toss it back with the rest of the curds. (You could not do this in a commercial operation and would have to toss it.) But it is my cheese and I wear gloves and have sterilized the end of the pH meter with a weak bleach solution and rinsed it well.
In the pressing I depress the cheese with the pH probe before I flip it. The depression will heal when the cheese is flipped but may leave a small mark. Since I have taken several readings on the wheel while pressing I have a great feel for the pH drop versus time and estimate when the goal pH will be reached. I don't bother with the final reading which would leave a dent in the cheese.
Your pH meter is vital to making reproducible cheeses that age into what you are striving for. I suggest that you "over measure" on your first several cheese makes until you get a feel for what happens to the pH over time. You will find that the steep drop occurs from about 6.1 to 5.1 or so but the time it takes to get there depends upon the amount, type of starter used and the ripening temperature. Ideally, you want the cheese to be fully pressed before the goal pH is reached. It is interesting to also measure the pH of the drained whey at the same time as you measure the cheese itself. You'll see how fast the two measurements differ.
Finally, it is important to have your saturated brine solution cool and ready to go so that you can brine the cheese as close to goal pH as possible.