Once you have made the polar decomposition, it is sufficient to find the Haar measure on the *compact* symplectic group. This can be calculated starting from your favorite parameterization $U(\{\alpha_n\})$ of the unitary symplectic matrix $U$, via the metric tensor,

$$g_{mn}=-{\rm tr}\,U^{\dagger}(\partial U/\partial\alpha_m)U^{\dagger}(\partial U/\partial\alpha_n),$$

and then the Haar measure is $d\mu= \sqrt{{\rm det}\,g}\prod_n d\alpha_n$.

Alternatively, you can use a computer to generate random matrices with the desired measure, as explained by <A HREF="http://arxiv.org/abs/math-ph/0609050">Franco Mezzadri.</A>