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 postmerger remnants. The model consists of three exponentially damped sinusoids with a linear frequency-drift term. We test the model against nine equal-mass numerical-relativity simulations selected for emission of gravitational waves for ≳25 ms. The median fitting factors between the model waveforms and numerical-relativity simulations exceed 0.90. We detect remnants at a postmerger signal-to-noise ratio of ≥7 using a Bayes-factor detection statistic with a threshold of 3000. We can constrain the primary postmerger frequency to ±1.21.4% at postmerger signal-to-noise ratios of 15 with an increase in precision to ±0.20.3% for postmerger signal-to-noise ratios of 50. The tidal coupling constant can be constrained to ±129% at postmerger signal-to-noise ratios of 15, and ±5% at postmerger signal-to-noise ratios of 50 using a hierarchical inference model.