Two important points to add: The word "solemnization" is never used in the US We would use "the marriage was solemnized", or better, "they solemnized their vows" , in the verb form. As said before, even in this form it is an uncommon word. You would almost never hear it spoken, but it does appear in writing.

In many countries in continental Europe (and probably elsewhere) marriages must be conducted by civil (government) authorities, usually in the local town hall or a registry office. After being married in the eyes of the law, if the couple are religious, they then attend a marriage ceremony conducted by a religious celebrant in their place of worship. This is what is generally understood as "solemnising" the marriage according to the couple's religious beliefs. In many English speaking countries there is no separate "civil" ceremony and couples and the religious ceremony is valid for civil and religious purposes. In these countries, people who do not wish to have a religious ceremony can attend a civil ceremony or arrange for an authorised marriage celebrant to perform the ceremony at the couple's home or indeed anywhere!

Well, a wedding ceremony is a solemnization. And I think that a marriage solemnization would be the same as saying "a wedding". The thing is, we don't really use the word "solemnization" very much. it is very uncommon. We usually just refer to a wedding ceremony.