  Binary neutron star mergers are rich laboratories for physics, accessible
with ground-based interferometric gravitational-wave detectors such as the
Advanced LIGO and Advanced Virgo. If a neutron star remnant survives the
merger, it can emit gravitational waves that might be detectable with the
current or next generation detectors. The physics of the long-lived post-merger
phase is not well understood and makes modelling difficult. In particular the
phase of the gravitational-wave signal is not well modelled. In this paper, we
explore methods for using long duration post-merger gravitational-wave signals
to constrain the parameters and the properties of the remnant. We develop a
phase-agnostic likelihood model that uses only the spectral content for
parameter estimation and demonstrate the calculation of a Bayesian upper limit
in the absence of a signal. With the millisecond magnetar model, we show that
for an event like GW170817, the ellipticity of a long-lived remnant can be
constrained to less than about 0.5 in the parameter space used.
