Is there an equivalent to "agnate" for the maternal line?

An "agnate" (Used both as a noun and adjective) is a person descended from the same male ancestor as another, through the male line. A "paternal kinsman" is also a way of defining "agnate."

http://www.thefreedictionary.com/agnate
http://www.merriam-webster.com/dictionary/agnate

Is there a similar word meaning a relative through female line, a "maternal kinsman"?

Solution 1:

The word you're looking for is enate.

From The Free Dictionary:

e·nate (ĭ-nāt′, ē′nāt′) adj. 1. Growing outward. 2. also e·nat·ic (ĭ-năt′ĭk) Related on the mother's side. n. A relative on one's mother's side.

Solution 2:

Maybe "cognates"? Look at this:

...persons who are related through females are not agnates but are otherwise relatives (cognati, “cognates”) by natural law. Thus, the relationship between an uncle and the son of his sister is not agnate but cognate. Likewise, the son of an aunt on my father’s or mother’s side is not my agnate but my cognate; and in turn, of course, I am related to him by the same rule.

A Casebook on Roman Family Law  
By Bruce W. Frier and Thomas A.J. McGinn

Solution 3:

Matrilineality is the tracing of descent through the female line.

• In a matrilineal descent system, an individual is considered to belong to the same descent group as her or his mother. This matrilineal descent pattern is in contrast to the more common pattern of patrilineal descent from which a family name is usually derived.

• The matriline of historical nobility was also called her or his enatic or uterine ancestry (corresponding to the patrilineal "agnatic" ancestry).

• In some traditional societies and cultures, membership in their groups was – and, in the following list, still is if shown in italics – inherited matrilineally. Examples include the Cherokee, Choctaw, Gitksan, Haida, Hopi, Iroquois, Lenape, Navajo and Tlingit of North America.

(Wikipedia)