Single-arm pressing exercises should be part of a well-rounded training program. They help create muscular balance and they develop your core due to the added stability requirements of offset loading.
The problem with unilateral pressing? Many lifters get lazy on the side they're not working and lose tightness throughout the lift. This forces them to compensate through the torso which puts undue stress on the spine if the core isn't braced properly.
As an example, here's a video of a very rough looking one-arm overhead press with absolutely zero attention paid to the unused arm:
This lift looks awkward and ugly. I could very easily tweak my back due to the lack of whole-body tightness.
The Simple Fix
Stick your opposite arm out to the side, make a fist, and squeeze as hard as you can. Do this not only for your press, but for any unilateral exercise where you have one hand free.
Why This Helps
Squeezing your fist revs up your nervous system. This aids in the recruitment of the motor units needed to successfully complete a heavy lift.
When the brain feels your muscles stabilize the weight, it lets the body know it's safe to output massive amounts of force without the risk of instability occurring. Your tightened fist will cause tightness throughout the core and upper back on both sides of your body. This allows for a better transfer of force through your kinetic chain.
Use This Concept With All Your Lifts
When performing any lift, grip strength is key to motor unit activation and whole-body tightness. With any heavy press, pull, squat, hinge, or carry, squeeze the bar as hard as possible to improve your mind-muscle connection and maximize force output.