When it comes to the Native American part, even if it comes back 0% it doesn't mean there's a lie in your family. I've learned that most North American Native tribes have not given their DNA samples to these companies, Chiefs have strictly forbidden it. So the tests are mostly comprised of samples from South American Natives (huge difference, since South America is more like Mexico, etc. -- not the organized tribes of the states).
So if it says 0% , don't curse out Grandma

she may not be lying.
When it comes to NA I would say the best option is traditional genealogy, if the heritage is close enough to you ,there should be some evidence that you can find within Censuses, etc. It's best to do these things while you still have Grandma around to help, they're usually the closest person we have to the past. (Unless we're blessed enough to still have our Great Grandparents alive.) They're really helpful with information, names, etc.
But as we know many of us have stories "having Indian up in me".

so it's healthy to be a bit skeptical until you're able to confirm.