Rohloff HG/IG Sprocket Checker is marginally effective on chainrings too. By eye the fins get to be thin and asymmetric (shark teeth that were mentioned). The space between the teeth becomes box-like. Outer ring gets only slowly worn out, so you can use its a reference for how the teeth should look like when not worn. In terms of how the operation is affected, the leading tooth or teeth begin to do all work, rather than the work being spread out, accelerating the wear of the teeth and chain.
What I look at, especially with chain stretch is an elongated notch indicating signs of wear, then looking at the pulling edge of the teeth, on a new ring, it should go almost vertical. On a badly ring, it is sloped, allowing the chain to ride high, which causes lots of problems (increases the diameter of the ring, effectively increasing the spacing between teeth, and thus a shorter chain will eventually pop over the top and skip.