Like rainbowgardener, I just put the cracked open eggshell halves in the compost pile/bin.
If I'm feeling extra industrious, I grind up some eggshells and put them in my vermicompost bin for the worms, but they need them to be powdered I heard or they can get hurt. I sometimes cheat and put entire cracked shells in there, and they manage to slither around or curl up inside the half shell.
When I have Bokashi bin fermenting, I also add crushed (but NOT ground) eggshells.
So I'm not entirely sure how it would work for container plant soil. But I think they would definitely break down faster as ground up powder, and if the container soil is live with microorganisms.
I believe eggshells would also be source of nitrogen and phosphorous. Some sulfur, too.
Another source of calcium would be seashells and shellfish. Again, I just use them as various composting ingredients, but when I find the clam and oyster shells and lobster and crab claws that tend to remain intact in the compost, I put them under (in the bottom of planting hole for) favored plants like paste type tomatoes that need the calcium more.
In Bokashi fermenter, which is an acidic environment, the shells break down faster. I think you could do the same by "pickling" the shells in vinegar, but then you would need to neutralize the acid somehow before giving it to the plants. I wonder what would happen if you put the ground up eggshells in a jar and cover with vinegar? I suppose you could take the result and dilute -- like a spoonful to a bottle of water? I really don't know, but it seems like an idea that could use some experimentation.