Consort applies to the spouse who died first, and is generally used to refer to the wife. When called "the consort of John Smith," it means that Mrs. Smith died first and that Mr. Smith then became a widower -- the Relict.
The word consort is the opposite of the word relict in the sense that a marriage is a consortium of husband and wife, hence each is a consort only while the union survives. The survivor of the marriage becomes the relict of that union.
Source: Black's Law Dictionary, 4th Edition.