Жениться / пожениться
I have been asked which words to use to describe marriages between two males or two females. Such marriages are not legal under Russian law, but how do the Russians talk about such marriages in other countries where they are legal?

Clearly they cannot use выйти замуж either for two males or for two females.

Жениться / пожениться may be used for either, but заключать / заключить брак (to enter into a contract of marriage) or расписываться / расписаться (to sign a (marriage) contract) may be preferred.