Balancing on the blocks...

Are you doing a grab start or a track start? I find I have much more stability with the track start and it is easier on my back. You want to be really warmed up and loose before you start practicing starts and certainly want to be really warmed up and loose before starting in a meet

in terms of stretching, I stretch after each swim. For starts, I think particular emphasis on hamstring stretches is useful. For balance, I practice standing on one leg, a couple of times a week, first with eyes open, and then with eyes closed. I can’t stand very long on one leg with eyes closed, but I’m working on it.

In addition to stretching, I suggest some strengthening exercises such (1-2 sets of 15 with or without hand weights):

• Box Step-ups - these will strengthen your quads.  Look for 12" step ups.  Don't worry about lifting your knee like the video. If you can't find a box, find stairs.
• Lateral Box Step ups - This will help with balance and strength
• Lunges - both forward, backward, and laterally.
• Deadlifts - with or without weights.  These will strengthen your lower back and glutes which are important to stability
• Calf raisers - strengthening the calves will make it easier to step up on blocks and help you push off the blocks.

As Allen mentioned, try the track start which is the same as a grab start, but with one foot forward and one back instead of both feet at the front of the block.

If you have neuropathy, this will mess with your balance, so I second what Allen mentioned about one leg balancing (10 x 15-20 seconds) will help as well.  Eyes closed is tough!

Thanks all.  Really appreciate the suggestions!

3URXX different facilities will have different blocks so it makes it hard to prepare for specific venues. In general, if it is during a meet, have a teammate or timer help you get on the block just to be safe. 
Practicing standing on one leg and moving the other leg up and down is a good exercise. Once you are confident in that, do one-legged squats where you only go down about 4-6 inches and then push back up on one leg to strengthen as well as solidify balance. 

3URXX,

I have been thinking more about about the unsteadiness.  I feel it as well and have a couple of suggestions I will follow myself:

• As we get older, for a variety of reasons, we spend less time with our body weight on the balls of our feet.  Be it walking with shorter strides or climbing stairs with our entire foot on the stair tread.  This leads to weaker, less flexible ankles and calves.  To offset this, spend time focusing on engaging your ankles and calves by planting only the ball of your foot on stair treads, walking with a full stride that requires a slight push off with the ball of your foot.  Heck, walk around on the balls of your feet.
• All of our answers focused on leg strength, but being unsteady on the blocks also involves the bending over motion.  So, practice the movements on the block while you are standing on a hard floor.  Place your right/left foot 12-15" ahead of your other foot, put weight on the balls of your feet, and bend over like you are "taking your mark" with your hands/fingers touching the floor in front of your front foot. Practicing this will strengthen your lower back, show you the hamstring tightness that Allen mentioned, and generally improve your balance as Kyle and Allen mentioned.  Work up to 10x.  Then, try it with your eyes closed. 

If you have access to a gym that has BOSU Sport Balance trainers - try these as they will improve your balance and ankle/calf strength.