Although it is somewhat old fashioned and outdated, it is still called the state of matrimony. The only problem today is that the estate no longer presumes or expects a woman to be a mother. Indeed, there is great delight in the suggestion that the estate not only does not require children but is perhaps better if there are no children. You can thank the creators of reliable birth control methods to make this all possible.
Oddly enough, the counterpart to matrimony, patrimony, does not quite mean the same thing. Perhaps it should but its history is decidedly different. From the mid-14th century, patrimoine, "property of the Church," also "spiritual legacy of Christ," and from Old French patremoine meaning "heritage," and deriving directly from Latin patrimonium "a paternal estate, inheritance from a father." The roots are similar, from pater (genitive patris) "father" (see father (n.)) + -monium, suffix signifying action, state, condition, and so it could mean the condition or estate of being a father. However, English law with its "right or property inherited from a father or ancestors" is the primary sense of it -- a curious contrast to matrimony. While matrimony is associated with marriage and children, patrimony is associated with property inherited from your father -- despite its similar roots.
I guess we use words all the time without actually thinking about their origins or how their usage sometimes betrays what the words themselves mean literally. In this case the matrons no longer wish to be mothers and they have the vocal and visible support of patrons who have an equal disdain for fatherhood. And there you have it. The sate of affairs today.