  Working with a general class of linear Hamiltonian systems on $[0, 1]$, we
show that renormalized oscillation results can be obtained in a natural way
through consideration of the Maslov index associated with appropriately chosen
paths of Lagrangian subspaces of $\mathbb{C}^{2n}$. We verify that our
applicability class includes Dirac and Sturm-Liouville systems, as well as a
system arising from differential-algebraic equations for which the spectral
parameter appears nonlinearly.
