Detection and parameter estimation of binary neutron star merger remnants can shed light on the physics of hot matter at supranuclear densities. Here we develop a fast, simple model that can generate gravitational waveforms, and show it can be used for both detection and parameter estimation of post-merger remnants. The model consists of three exponentially-damped sinusoids with a linear frequency-drift term. The median fitting factors between the model waveforms and numerical-relativity simulations exceed 0.90. We detect remnants at a post-merger signal-to-noise ratio of ≥7 using a Bayes-factor detection statistic with a threshold of 3000. We can constrain the primary post-merger frequency to ±^(1.4)_(1.2)% at post-merger signal-to-noise ratios of 15 with an increase in precision to ±^(0.3)_(0.2)% for post-merger signal-to-noise ratios of 50. The tidal coupling constant can be constrained to ±⁹₁₂% at post-merger signal-to-noise ratios of 15, and ±5% at post-merger signal-to-noise ratios of 50 using a hierarchical inference model
