  A square complex matrix $A$ is called (skew) $J$-Hamiltonian if $AJ$ is
(skew) hermitian where $J$ is a real normal matrix such that $J^2=-I$, where
$I$ is the identity matrix. In this paper, we solve the Procrustes problem to
find normal (skew) $J$-Hamiltonian solutions for the inverse eigenvalue
problem. In addition, a similar problem is investigated for normal
$J$-symplectic matrices.
