  Let $K$ be a number field, let $A$ be a finite-dimensional semisimple
$K$-algebra, and let $\Lambda$ be an $\mathcal{O}_{K}$-order in $A$. We give
practical algorithms that determine whether or not $\Lambda$ has the stably
free cancellation property (SFC). As an application, we determine all finite
groups $G$ of order at most $383$ such that the integral group ring
$\mathbb{Z}[G]$ has SFC.
