Q. I offered to give a kidush in shul. Is there a special inyan to give it on Shabbos Nachamu?

A. Indeed there is, Nitei Gavriel (Bein Hametzorim 2: 77: 2: p.556) quotes Ben Shoeiv, (a talmid of the Rashbo) on Voeschanan and Yosef Ometz (779) that it is a mitzva to rejoice on this Shabbos more than in other Shabbos in the year. Maharil mentions that people should rejoice and trust on the consoling and comforting of Hashem and the promptly coming of the geulah.
Ritva (Taanis 30b) writes that there is a minhag to make a seuda on the Shabbos after Tisha Beav.
Horav Shlomo Miller Shlit”a added, that the special simcha celebrating the nechama and comfort on Shabbos Nachamu applies to the ones that engaged properly and correctly on the avelus and mourning of the prior three weeks. As our sages teach (Taanis 30b); “Whoever grieves for Yerushalaim, merits to witness her joy”

Rabbi A. Bartfeld as revised by Horav Shlomo Miller Shlit’a