When bouldering, knee pain can arise specifically from incorrect falling technique and uneven weighting between feet.
Drop and roll!
As climbers we all know that we really should roll every time when coming off the wall. However, many of us develop bad habits. Squatting after falling from a height is not a safe falling technique, even if it works out 99% of the time. Falling in this way is asking for some trouble down the line.
Uneven weighting
Uneven weighting comes from a lack of awareness about climbing technique and possibly from weak muscle groups too. Consistently favouring one leg over the other naturally leads to strain by overuse. Breaking the habit will require a conscious effort. You can treat it like any other climbing skill and train it during warmups - when you’re more controlled and rested - to automate it. The goal here is to reduce excess strain on your favoured knee, however consultation and rehabilitation from a professional is always recommended when knee pain occurs.
Avoid inflammatory movements
Some moves in climbing may exacerbate knee pain more than others. When in recovery, it’s best to avoid these. Drop knees and knee bars spring to mind when thinking of moves that apply stress to the joint, and these should be avoided. Some other moves that can be strenuous include rockovers, toe hooks, and heel hooks. Rockovers can be difficult to regulate weight on, and toe and heel hooks require a lot of tension through the joint. This information may be useful to your physio when talking about gradually coming back into climbing. Set rules around avoiding these moves entirely to avoid further injury during recovery.
Building strength
We deload the stress on the knees by working on the joints above and below, strong and well functioning ankles and especially hips will absorb force a lot better than weak ones.
Split squats are an Axis favourite when it comes to improving both at the same time. Single leg deadlifts are great for balance too. You can find both of these below.
Split Squats: https://youtu.be/fxFJtFtEcDo
Single Leg Deadlift: https://youtu.be/nIyzqkwBGUM