  Port-Hamiltonian systems result from port-based network modeling of physical
systems and are an important example of passive state-space systems. In this
paper, we develop the framework for model reduction of large-scale
multi-input/multi-output port-Hamiltonian systems via tangential rational
interpolation. The resulting reduced-order model not only is a rational
tangential interpolant but also retains the port-Hamiltonian structure; hence
is passive. This reduction methodology is described in both energy and
co-energy system coordinates. We also introduce an $\mathcal{H}_2$-inspired
algorithm for effectively choosing the interpolation points and tangential
directions. The algorithm leads a reduced port-Hamiltonian model that satisfies
a subset of $\mathcal{H}_2$-optimality conditions. We present several numerical
examples that illustrate the effectiveness of the proposed method showing that
it outperforms other existing techniques in both quality and numerical
efficiency.
