  In this article we investigate the problem of computing Tamagawa numbers of
CM tori. This problem arises naturally from the problem of counting polarized
abelian varieties with commutative endomorphism algebras over finite fields,
and polarized CM abelian varieties and components of unitary Shimura varieties
in the works of Achter--Altug--Garcia--Gordon and of Guo--Sheu--Yu,
respectively. We make a systematic study on Galois cohomology groups in a more
general setting and compute the Tamagawa numbers of CM tori associated to
various Galois CM fields. Furthermore, we show that every (positive or
negative) power of $2$ is the Tamagawa number of a CM tori, proving the
analogous conjecture of Ono for CM tori.
