We present the addition of nebular emission from the narrow-line regions (NLR) surrounding active galactic nuclei (AGN) to beagle (BayEsian Analysis of GaLaxy sEds). Using a set of idealised spectra, we fit to a set of observables (emission-line ratios and fluxes) and test the retrieval of different physical parameters. We find that fitting to standard diagnostic-line ratios plus [O ii] λ3726, λ3729/[O iii] λ5007, Hβ/Hα, [O i] λ6300/[O ii] λ3726, λ3729 and Hα flux, degeneracies remain between dust-to-metal mass ratio ($\xi _\rm {d}^{NLR}$) and ionisation parameter ($U_\rm {s}^{NLR}$) in the NLR gas, and between slope of the ionizing radiation ($\alpha _{pl}$, characterising the emission from the accretion disc around the central black hole) and total accretion-disc luminosity ($L_\rm {acc}$). Since these degeneracies bias the retrieval of other parameters even at maximal signal-to-noise ratio (S/N), without additional observables, we suggest fixing $\alpha _{pl}$ and dust-to-metal mass ratios in both NLR and H ii regions. We explore the S/N in Hβ required for un-biased estimates of physical parameters, finding that S/N(Hβ) ∼ 10 is sufficient to identify a NLR contribution, but that higher S/N is required for un-biased parameter retrieval (∼20 for NLR-dominated systems, ∼30 for objects with approximately-equal Hβ contributions from NLR and H ii regions). We also compare the predictions of our models for different line ratios to previously-published models and data. By adding [He ii] λ4686-line measurements to a set of published line fluxes for a sample of 463 AGN NLR, we show that our models with $-4<\hbox{$\log U_{s}^{NLR}$}<-1.5$ can account for the full range of observed AGN properties in the local Universe.