I am thinking of two baptized persons who were ready to be married but for some reason find themselves in such a situation with no hope of relief for many months.
Since a Christian couple confers the sacrament of matrimony upon each other, a priest is not absolutely necessary for a couple to marry. A deacon can preside at a marriage, and so can a designated layperson in the absence of a priest or deacon. If there is no representative of the Church—say, in the event of the martyrdom and/or exile of all the clergy, as happened centuries ago in Japan—the couple can marry each other in the presence of witnesses. If stranded alone on a deserted island, and keep in mind that I am speculating here, I would guess that the couple could marry each other even in the absence of any witnesses. Of course, once the situation is resolved and the couple is restored to a situation in which clergy is available, they should seek to regularize their marriage in the eyes of the Church.