You say it right, you "catch" the kick, which means you pick a spot on the shin you want to catch it with, and you meet it up, like you are using a glove and catching a ball. As to how high you bring it up depends on how high the kick is. I'm not super experienced with this myself, but I did start doing it in padwork when I had a banged up shin, and the train was fond of whacking me back with a kick. I just started catching the kick just below the kneecap, or even with the point of the knee, gently. For me, I'd fold the leg a bit to give the knee support. It is very hard when bent. There are some really good things about it. The first is that you are practicing accuracy. People don't think of blocks needing accuracy, but they do. It's usually just "Get your block up!", but all the greats were super accurate with their checks. They aren't using the whole shin. Trying to catch it in a specific part of the shin is super productive, and will give you confidence in your checks over time.
As to hurting your partner, well, they are hurting you. Not intentionally, but yeah, it's hurting you. The whole point of sparring without shin guards, or the whole benefit, is that it teaches you control and feeling. If you are catching kicks up on the thick high part of your shin, or catching with the point (a little), they just have to pull their kicks, gain control. It's sparring, not whacking. You don't have to spear them with the knee, just catch it.
I'm not even saying you could/should do this. But there are some good ideas why it might make sense in your situation. And it could be fun. In terms of Muay Thai you don't want to be catching kicks all day, in the long term.