[en] We present an effective, low-dimensionality frequency-domain template for the gravitational wave (GW) signal from the stellar remnants from binary neutron star (BNS) coalescence. A principal component decomposition of a suite of numerical simulations of BNS mergers is used to construct orthogonal basis functions for the amplitude and phase spectra of the waveforms for a variety of neutron star (NS) equations of state and binary mass configurations. We review the phenomenology of late merger/post-merger GW emission in BNS coalescence and demonstrate how an understanding of the dynamics during and after the merger leads to the construction of a universal spectrum. We also provide a discussion of the prospects for detecting the post-merger signal in future GW detectors as a potential contribution to the science case for third generation instruments. The template derived in our analysis achieves $><!--\; >\; -->90\mathrm{\%<!--\; \%\; -->}$ match across a wide variety of merger waveforms and strain sensitivity spectra for current and potential GW detectors. Using a simple Monte Carlo simulation, we find a preliminary estimate of the typical uncertainty in the determination of the dominant post-merger oscillation frequency $f_{\mathrm{p}\mathrm{e}\mathrm{a}\mathrm{k}}$ of $\mathrm{\delta <!--\; ??\; -->}{f}_{\mathrm{p}\mathrm{e}\mathrm{a}\mathrm{k}}\sim <!--\; ???\; -->138\mathrm{H}\mathrm{z}$. Using recently derived correlations between $f_{\mathrm{p}\mathrm{e}\mathrm{a}\mathrm{k}}$ and the NS radii, this suggests potential constraints on the radius of a fiducial NS of ∼429 m. Such measurements would only be possible for nearby (∼30 Mpc) sources with advanced LIGO but become more feasible for planned upgrades to advanced LIGO and other future instruments, leading to constraints on the high density NS equation of state which are independent and complementary to those inferred from the pre-merger inspiral GW signal. We study the ability of a selection of future GW instruments to provide constraints on the NS equation of state via the postmerger phase of BNS mergers. (paper)