Númenor: Númenor is easy and hard. Hard because Tolkien never worked out to his own satisfaction what the amended law of succession really said; easy because in any version it provided for Ruling Queens, of which there were four. And of course Ar-Pharazôn had no right to the throne at all, but claimed it as spouse of his royal wife, with whom he ruled jointly like William & Mary.
Rohan: Rohan unquestionably did not apply the full-blown Salic Law as it was interpreted in France and Germany, which held not only that women could not succeed, but could not even pass the succession to a male. (France and England warred for over a century on this point- who says legal quibbles aren't a big deal?
).Whereas in Rohan we have two clear cases of Kings inheriting through the female line: Frealaf (Helm's successor) and Éomer were their predecessors' sister-sons. What we don't know is whether the warrior Rohirrim would have permitted a Ruling Queen. Unfortunately Tolkien doesn't provide enough data: although we know Théoden's sister Theodwyn was dead by 3019, he does not tell us whether Helm's daughter and sister predeceased him or not, and therefore whether they were passed over in favor of the male heir.
(Although Théoden designated Éomer as his heir (twice) before he died, the impression I get is that he was just putting the succession beyond doubt, even though it was already assumed).
Arnor: Insufficient data. The male Line of Isildur was unbroken, father to son, for three millennia (whoa!)
Gondor: In Gondor, however, I think there is evidence for the Salic Law, a break with the law of Númenor. It isn't merely that Gondor happened never to have a ruling Queen; but that in the one case where we know the situation arose, the woman was passed over. This was Firiel daughter of Ondoher. In the succession crisis of 1944, we know that Gondor rejected Arvedui's claims in right of his wife and of his own descent from Elendil; but note, also, that Firiel as the only surviving child of the late King should have been Queen in her own right, regardless of her husband's ambitions, unless she were debarred by gender.
There are additional hints in the history of Gondor: for instance, we know that the House of the Stewards was of royal blood- yet had no cognizable claim on the throne. How could that be, unless the royal descent was on the distaff side? And in the crises of 1944 and 2002, the problem was not that there were no royal descendants, but none with a valid claim: again, I suggest, because they descended from Anárion in the female line.
