We had a class project in my college grammar class where we had to bring in examples of bad grammar or weird headlines in newspapers and magazines, or funny uses of grammar on billboards or signs.
One of my favorites was, "Nervous Charlie's Fireworks and Beer" which was a billboard I saw on the Interstate. I loved that. So I guess that would be classified as an authentic assessment type of test.
I've taken all kinds of grammar tests, including the composition kind and diagramming kind. If you know what you're doing, they're not that difficult, but if you don't, you can get mixed up very quickly.