  For the cubic Schr\"odinger system with trapping potentials in
$\mathbb{R}^N$, $N\leq3$, or in bounded domains, we investigate the existence
and the orbital stability of standing waves having components with prescribed
$L^2$-mass. We provide a variational characterization of such solutions, which
gives information on the stability through of a condition of
Grillakis-Shatah-Strauss type. As an application, we show existence of
conditionally orbitally stable solitary waves when: a) the masses are small,
for almost every scattering lengths, and b) in the defocusing, weakly
interacting case, for any masses.
