  We consider a two-planet system, which migrates under the influence of
dissipative forces that mimic the effects of gas-driven (Type II) migration. It
has been shown that, in the planar case, migration leads to resonant capture
after an evolution that forces the system to follow families of periodic
orbits. Starting with planets that differ slightly from a coplanar
configuration, capture can, also, occur and, additionally, excitation of
planetary inclinations has been observed in some cases. We show that excitation
of inclinations occurs, when the planar families of periodic orbits, which are
followed during the initial stages of planetary migration, become vertically
unstable. At these points, {\em vertical critical orbits} may give rise to
generating stable families of $3D$ periodic orbits, which drive the evolution
of the migrating planets to non-coplanar motion. We have computed and present
here the vertical critical orbits of the $2/1$ and $3/1$ resonances, for
various values of the planetary mass ratio. Moreover, we determine the limiting
values of eccentricity for which the "inclination resonance" occurs.
