We study how small perturbations of a skew-symmetric matrix pencil may change its canonical form under congruence. This problem is also known as the stratification problem of skew-symmetric matrix pencil orbits and bundles. In other words, we investigate when the closure of the congruence orbit (or bundle) of a skew-symmetric matrix pencil contains the congruence orbit (or bundle) of another skew-symmetric matrix pencil. This theory relies on our main theorem stating that a skew-symmetric matrix pencil A-\lambda B can be approximated by pencils strictly equivalent to a skew-symmetric matrix pencil C-\lambda D if and only if A-\lambda B can be approximated by pencils congruent to C-\lambda D.