How does the romantic period relate to the poem "Ozymandias"?

This is an interesting question just because it's not a usual thing for teachers to focus upon the Romantic characteristics in regards to this poem.  However, they fit really well!  This is especially true in the Romantic characteristics of importance of the common life as opposed to royalty/government, emotion, and nature (while it focuses less on the supernatural forces often seen within Romanticism).

First, let's concentrate on the importance of the "common man" instead of royalty, gentry, or upper classes.  Take this quotation:

Two vast and trunkless legs of stone
Stand in the desert. Near them on the sand,
Half sunk, a shatter'd visage lies, whose frown
And wrinkled lip and sneer of cold command
Tell that its sculptor well those passions read
Which yet survive, stamp'd on these lifeless things

There is a statue here, yes.  It stood for an "important" ruler of the past, yes.  However, the statue lies in ruins.  The legs are "trunkless."  It is only a "shatter'd visage."  It is also "half sunk" where only the sculptor's idea of his age and severity stand according to the "wrinkled lip" and the "sneer of cold command."  Even though there is no direct statement of the common man here, what is clear that there is only a negative image presented of the ruler Ozymandias.  This lack of honor for a ruler is certainly characteristic of Romanticism mostly in that it contradicts the usual characteristic:  value of the simple life of a commoner.

Next, are the focus on emotion both of disgust (from the speaker) and from Ozymandias himself (due to his expression on the stone).  You can see the disgust from the speaker in his description from the above paragraph.  Further, you can see the emotion (or perhaps I could say, the pointless emotion?) that is expressed here:

"My name is Ozymandias, king of kings:
Look on my works, ye Mighty, and despair!"

There is no better punctuation for an emotional interjection than an exclamation point!  The irony is that Ozymandias' exclamation, as well as the emotion behind it, is completely extinct.

Finally, we have to look at the obvious characteristic of Nature's sheer power.  This may be the BEST example in Romanticism, actually.  Although it's not in Nature's beauty of awesomeness, but in Nature's DESTRUCTIVE ability to tame the power of man.

Two vast and trunkless legs of stone
Stand in the desert. Near them on the sand,
Half sunk, a shatter'd visage lies, ...
Nothing beside remains: round the decay
Of that colossal wreck, boundless and bare,
The lone and level sands stretch far away.

The "powerful" man here is "trunkless," further the parts of Ozymandias that remain are "shatter'd."  It is a "colossal wreck."  Why?  NATURE has made Ozymandias that way.  If you look in between the lines, the part of nature that is DEATH has eliminated Ozymandias, a tyrannical ruler, from the planet.  The last line is fitting.  It is about the eternal nature of Nature.  It isn't Ozymandias that is "lone" and stretching "far away."  No.  It is Nature's sand, eliminating the power of the despot.