I don't think there's ever harmonic certainty. Just ask a jazz musician. The closest thing I can think of is when the chord at hand bears a strong resemblance to something you know, or forms the expectation for something you reasonably expect.
I haven't found it on Youtube, but I heard of a demonstration that Wynton Marsalis once gave in which he used piano keys to convincingly make the sound of a large bell. By striking the listener's recognition of the bell, he really "nailed it"--- he made a certain sound that would be less somehow if you added (rather than subtracted) a seventh or third.
During normal choral or orchestral composition, anything is uncertain if what follows will cause the ear to reinterpret it. This was the device Beethoven used at the starting point of his Ninth Symphony. Study a Bach fugue and you will see this over and over and over again.
But when rock guitarists use power chords (I-V-VIII) it doesn't matter that there's no third: the completeness and certainty come from the distortion, making the timbre a thing you know and recognize: jumjumjumjum....
I think that every musical idea is more or less recognizable, from a simple melody like Twinkle Twinkle to a peculiar turn of Adele's voice, the "hook" of your favorite symphony, and even the drum pattern from "Exit Light" by Metallica.
Anything you do on top of a musical idea will put it into a new light. You will probably get further doing this with simple things, although old-school hip-hop artists would rap right over samples of their favorite songs to great effect.