I learned a new exercise (new to me anyway) for strengthening the upper leg, securing the lower leg, and finding your seat bones all in one exercise. It's simple but certainly not without pain. Here's what you do.
Hike your stirrups up so high that you need a leather hole punch a few holes above your last stirrup leather hole. Get on horse. Assume a half seat position. Your butt should almost touch the saddle but still clear it. Most of us lesser mortals will initially need to hold mane to keep this position. Walk around in that position until you can no longer hold it. When you can handle more torture, do it at the trot and then canter. With your stirrups hiked up, there is literally nothing keeping you up there but your lower leg, so it sure as heck better be secure. When you sit between sets, you'll notice that your thighs are so far above the saddle, you're sitting solely on your seat bones, which is great for balance.
I did this exercise once and a day later was posting 100% better using my thighs correctly instead of posting off my stirrups. Floppy dying fish legs are quickly leaving. Just wanted to share since everyone seems to want stronger legs, and this is a fantastic exercise. Have fun!