Back in feudal days, in exchange for a fief, such as a tenancy of land, and for his protection, a man would formally and publicly acknowledge himself the vassal of his lord. The vassal would solemnly vow to the lord both fealty (fidelity) and that he would fulfill certain obligations and duties. This ceremony was known as an homage, after the Old French word homme meaning "man." (来源：www.EnglishCN.com)

As feudalism became entrenched, homage developed another sense, too: "an act or payment done in meeting the obligations of vassalage." When the system of feudalism faded from the political landscape, homage proved too useful to discard. It stayed on in English with the sense "expression of high regard; respect" and established itself in the phrase pay homage.

Now we know the history of homage, we'll handle the issue of its pronunciation. We've been dropping the "h" sound, and that is indeed the most common pronunciation for homage these days. From the days of feudalism until the 18th century, the "h" in homage was silent (perhaps in tribute to its French ancestry). Then, for whatever reason, the "h" sound appeared.

So is one pronunciation considered correct and the other incorrect? Call it a homage to our inclusive language, but, no. Both pronunciations are acceptable.