  We systematically investigate $C^*$-norms on the algebraic graded product of
$\mathbb{Z}_2$-graded $C^*$-algebras. This requires to single out the notion of
a compatible norm, that is a norm with respect to which the product grading is
bounded. We then focus on the spatial norm proving that it is minimal among all
compatible $C^*$-norms. To this end, we first show that commutative
$\mathbb{Z}_2$-graded $C^*$-algebras enjoy a nuclearity property in the
category of graded $C^*$-algebras. In addition, we provide a characterization
of the extreme even states of a given graded $C^*$-algebra in terms of their
restriction to its even part.
