This all sounds very spiritual, mystical and woo-woo - and of course it is; by mainstream contemporary standards of public discourse - yet super-sensible perception is also pretty much an everyday occurrence for many (not all) people.
Super-sensible perception may be identified because we perceive something; yet we know that what are perceiving is not a part of the sensory data.
To show what I mean I will give examples from my personal experience.
When hearing great music, I am aware that what I most value is not in the composition, nor is it captured by the performance: it is not simply a product of sound perceived by hearing. This is a fact, and the fact is obvious - but not trivial. Even when the music is nothing but arpeggio block chords, as with the piece above.
When viewing a great painting (the above being of Salisbury Cathedral by John Constable) I feel far more than the depiction or the paint, is doing - there is a definite and solid sense of mystery about what I perceive.
My love he built me a bonny bower,
And clad it a’ wi’ lilye flour;
A brawer bower ye ne’er did see,
Than my true love he built for me.
There came a man, by middle day,
He spied his sport, and went away;
And brought the King that very night,
Who brake my bower, and slew my knight.
(The beginning of the Lament of the Border Widow, an anonymous Scottish-English Border Ballad.)
The above poetry is simple, crude, un-literate - the first verse uses many conventional and clichéd phrases, the second verse is literalistic in its description... Yet super-sensible perception tells me, with rock-solidity and stark factuality - that this poem is as beautiful and profound as can be told.
Please don't ask me to explain what on earth (or off it) The Little Prince story is about - I only know it is about much much more than my sense perceive.
5. Paranormal phenomena
A large majority of the population feel quite sure that some dreams mean something beyond the dream; or that they sometimes foresee future events; or that the sometimes experience telepathic communications - that such experiences are sometimes valid - and they equally sure that these valid experiences cannot always be explained by five-sense, 'objective' perception. I agree.
6. The night sky
When I look at the night sky, on a clear night (only on a clear night, with darkness between the stars) a can see a network of fine silver lines radiating from and joining the heavenly bodies, stretching across considerable segments of the sky: I see not so much a spray of detached stars, as a luminous gossamer web over the dome.
I know that I see these threads by super-sensible means - because they are not seen by other observers (i.e. they are not an optical illusion), they are not recordable by binoculars - yet the lines are there, quite definite; present but not originating from vision.
In sum, super-sensible perception is something common and everyday that most people experience already - they only need to notice it, take it seriously, and regard it as real.