  We define a family of Schroedinger Functional renormalization schemes for the
four-quark multiplicatively renormalizable operators of the $\Delta F = 1$ and
$\Delta F = 2$ effective weak Hamiltonians. Using the lattice regularization
with quenched Wilson quarks, we compute non-perturbatively the renormalization
group running of these operators in the continuum limit in a large range of
renormalization scales. Continuum limit extrapolations are well controlled
thanks to the implementation of two fermionic actions (Wilson and Clover). The
ratio of the renormalization group invariant operator to its renormalized
counterpart at a low energy scale, as well as the renormalization constant at
this scale, is obtained for all schemes.
