You can catch crab using a chicken leg and rope, no shit. Don't even need a net/cage.
My dad got bored one day and brought three chicken legs with us when we went fishing. He just tied it up to the fishing line and cast out. Reeled it in really slow, and once it got close enough, flung it onto land (I think only one let go).
He made his own trap from chicken wire and wood. Same bait. Its basically a cube with a funnel going in, so the crabs can't find the exit fast enough to escape. They aren't really hard to catch.
I've only caught one lobster. It was off a bridge, and a complete mistake, since the hook got caught in a hinge on one of its legs.