The plaintiffs say the missing people vanished after being arrested by Russian servicemen. They also said that the Russian authorities failed to effectively investigate the cases.
The relatives claimed that armed men took Aslanbek Astamirov, Alis Zubirayev, Ilyas Sagayev and Yunadi Sagayev from their homes in Urus-Martan and Chechen-Aul.
The Court ruled that the Russian authorities had violated a number of articles of the European Convention on Human Rights, including the right to life, a ban on torture and humiliation, the right to freedom and security and the right to effective legal protection.
The sum includes 140,000 euros in moral damages, 17,000 euros for material damages and 19,744 euros to cover Court expenses.
Around 20% of all complaints made to the Court in the past decade have involved Russia.
Chechnya saw two brutal separatist wars in the 1990s and early 2000s. Militant attacks remain fairly common in the troubled republic.
