The single-arm kettlebell press is one of the best ways to get more weight on your shoulders and into your presses. Take your max barbell strict press and half it. Most people find they're able to lift MORE than half per arm with a kettlebell.
Also, testing each arm individually is a great way to keep on top of developing imbalances. If you can press a considerably larger weight with one arm compared to the other, alter your programming to correct that before jumping into any strength programs.
Do It Right
The way you hold your kettlebell for pressing is extremely important, and not just for maximal strength gains and wrist health. Holding it incorrectly runs the serious risk of a kettlebell enthusiast punching you. (You know how they get.)
When you're pressing a heavy kettlebell, keep the weight as close to your body as possible. Think about bracing as if you were doing a one-rep max deadlift. The rack position is in front of your body, not at the side and definitely not resting on your shoulder.
The wrist position is extremely important too. If your wrist is extended backwards, your forearm won't be supporting the weight. You'll be limited in how much you can press and can even get injured. Roll your fist so that your knuckles are pointing to the ceiling and you have a neutral grip.