Are there any monarchial claimants for Armenia and Georgia?

Yes, there is an heir to the Georgian throne, HRH Prince Guiorgui Bagrationi de Mukhurani, a former race car driver who as king would be George XIV. Most of what I know about him comes from an interview in the July 1993 issue of Royalty magazine (which used to be much more interesting than it now is; I let my subscription drop after they started putting the likes of Angelina Jolie on the cover); I haven't heard much about him since then.

Prince George was born on February 22, 1944 and has two sons and a daughter from his first marriage and a son from his second marriage. (Both marriages were celebrated in the Orthodox Church.) He has been head of the ancient Georgian royal house, which ruled from the 3rd century A.D. until annexation by Russia in 1801, since the death of his father Irakly (1909-1977). His aunt, Princess Leonida (b. 1914), married longtime Romanov pretender Vladimir Kirillovich of Russia (1917-1992), so their daughter Maria Vladimirovna (b. 1953), the current claimant to the Russian throne, is his first cousin.

Otherwise he is not related to other European royalty, though his mother (who died giving birth to him) was an Italian aristocrat, Countess Maria Antonietta Pasquini.

I don't know about Armenia.

Source: Monarchy Forum