The coat of arms of the Russian royal family, the Romanovs, sported the black double-headed eagle, which also crops up in different colours in other Eastern European heraldry, such as the Austria-Hungary coat of arms. It also crops up (very batlike — black on red) in the Albanian flag.
Apparently the double-headed eagle specifically came to symbolise Imperial power in heraldry, as opposed to the single-headed eagles, which were more generally used for conventional royalty and kingdoms in that area of the world.
Going back further in time, the Holy Roman Empire (see the previous annotation) also used a double-headed eagle in the 15th century.