Obergefell v. Hodges was argued in front of the US Supreme Court today, and the audio transcript has already been released. The case will decide whether the federal government can force states to recognize gay marriage. One of the right-leaning justices (I think it was Alito) harped on the point that marriage has been universally defined as exclusively heterosexual "for millennia"—up until the last quarter-century or so. He pressed the lawyer arguing on behalf of gay couples to name a pre-modern society that considered homosexual marriage equally sacrosanct. She couldn't name one.
Do you folks know of any?
In technicality this might not be consider same-sex marriage, and it's more "pre-Western" than "pre-modern", but among the Sudanese Nuer, and I believe among the Igbo in Nigeria as well, women were allowed to marry other women and act as husbands in order to preserve a lineage inside the family or if there wasn't a suitable partner. However, I think that they might have been considered men from a social point of view; at least it's clear they saw gender in a more fluid way.
At least in the Western World, the concept of homosexuality as a distinct, lifelong orientation is really a modern concept, largely incompatible with premodern ideas about sexuality. In medieval and early modern European societies, the term "sodomite" was used for men who engaged in same-sex relations. I say men because same sex relations between women don't seem to receive the same consideration in existing records, save for truly exceptional cases.
The dominant model for male same sex relations in Europe was pederasty, that is, an older man having sex with a younger man (typically below the standard marriage age, frequently young "smooth-cheeked" adolescents). In these relationships it was expected that the older man would be the penetrator, the "active partner," and the younger man would be "passive" (the general belief in this period was that any sexual intercourse had an active and passive partner, rather than two mutually active partners as we understand it today). Exceptions to this model are extremely rare. Tolerance for this practice varied widely in medieval and early modern Europe. In some areas, the practice of sodomy could be very widespread indeed. Historian Michael Rocke estimates that as many as two thirds of the male inhabitants of 15th and 16th century Florence engaged in same sex relations at least once.
As homosexuality was not really a concept that premodern Europeans understood, it was generally expected that the "passive" young men would grow out of sodomy and take a wife of their own, and that older men who engaged in sodomy were simply expressing more generalized lust.
So, as far as premodern, post-classical Europe is concerned, Scalia is technically correct. But at the same time, sexual norms and ideas have changed so much over the course of centuries that I don't really see it as a meaningful question. But that's just my perspective
I drew heavily on Michael Rocke's Forbidden Friendships: Homosexuality and Male Culture in Renaissance Florence and Ruth Karras's Sexuality in Medieval Europe: Doing unto others for this answer. As far as non-western cultures, I'm not really sure, but I hope this answer shows that Scalia's question didn't really take into account additional cultural context.
Sorry for a Wiki citation, but the Siwa Oasis in Egypt apparently practiced commonplace homosexual marriage ceremonies, though I'm unsure how long these marriages lasted, or whether they reflected natural-born homosexuality as we understand it, or rather more fluid sexuality.
Similarly to what other posters mentioned about Europe, these marriages were between adult men and boys between the age of 12 and 18 years old. Again, I'm unsure what happens to their marriage once the boys reach adulthood. The people were evidently very comfortable and open with these relations as late as 1900, though, and have only more recently begun to suppress information regarding their past.