From Tolkien Gateway

Nárië (Nórui in Sindarin) was the sixth month of the year in the King's Reckoning and the Stewards' Reckoning of Gondor, following Lótessë, and preceding Loëndë (Mid-year's Day). In the New Reckoning it was the third month of the year, immediately preceding Cermië.

Nárië in the Kings' Reckoning and in the Stewards' Reckoning corresponded, for the most part, to Forelithe in the Shire Calendar (approximately modern 22 May through 20 June).[1]