What app is making my phone vibrate, without putting a corresponding notification up? There is an app I can't locate that is constantly making my phone vibrate. When it does, I immediately check the Notification Center. Nothing new there.

The vibrate could be a setting for an email application, or some other app. 

One thing to note, I always have my app on silent/vibrate.  I just unmuted it in the hopes that the sound will help me figure out what is going on. 

Question

How can I determine which app is sending rogue vibrations without any notification?
You may need to go through Settings → Notifications and check which apps have an Alert Style of None and Show in Notification Center disabled, but Sound toggled on.