  A cross-intersecting Erd\H{o}s-Ko-Rado set of generators of a finite
classical polar space is a pair $(Y, Z)$ of sets of generators such that all $y
\in Y$ and $z \in Z$ intersect in at least a point. We provide upper bounds on
$|Y| \cdot |Z|$ and classify the cross-intersecting Erd\H{o}s-Ko-Rado sets of
maximum size with respect to $|Y| \cdot |Z|$ for all polar spaces except
Hermitian polar spaces in odd projective dimension.
