The Gromov width is a symplectic invariant measuring the size of the smallest open ball that embeds symplectically. Foliations by pseudoholomorphic curves are a useful tool to find upper bounds on this number. However, finding such foliations for tangent bundles is initially challenging. Results by Albers, Frauenfelder and Oancea imply that, for example, if the Hurewicz map of the base manifold does not vanish, such foliations must exist. In this talk, we present how to construct explicit finite energy foliations in the case that the base manifold is a Hermitian symmetric space and use them to compute the Gromov width of suitable subsets of the tangent bundle.