Once you have made the polar decomposition, it is sufficient to find the Haar measure on the <a href="https://en.wikipedia.org/wiki/Symplectic_group#Sp.28n.29">compact symplectic group.</A> This can be calculated starting from your favorite parameterization $U(\{\alpha_i\})$ of the unitary symplectic matrix $U$, via the metric tensor,

$$g_{ij}=-{\rm tr}\,U^{\dagger}(\partial U/\partial\alpha_i)U^{\dagger}(\partial U/\partial\alpha_j),$$

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

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>