Previous observations have shown spatial covariances between microwave emission from Antarctic firn at 6 cm wavelength, physical firn temperature and firn-density stratification. Such observations motivate us to understand the physics underlying such covariances and, based on that understanding, to develop estimation methods for firn in which density, and therefore dielectric permittivity, varies randomly in discrete layers with mean thicknesses on the order of centimeters. The model accounts for depth profiles of the physical temperature, mean density and variance of random density fluctuations from layer to layer. We also present a procedure to estimate emission-model input parameters objectively from in situ density-profile observations, as well as uncertainties in the input parameters and corresponding uncertainties in theoretical brightness-temperature predictions. We compare emission-model predictions with ground-based observations at four diverse sites in Antarctica which span a range of accumulation rates and other parameters. We use coincident characterization data to estimate model inputs. At two sites, layered-medium emission-model predictions based on the most probable input parameters (i.e. with no model tuning) agree with observations to within 3.5% for incidence angles≤50°. Corresponding figures for the other two sites are 7.5% and 10%. However, uncertainties in the input parameters are substantial due to the limited length and depth resolution of the characterization data. Uncertainties in brightness-temperature predictions are correspondingly substantial. Thus brightness-temperature predictions for the last-mentioned sites based on only slightly less probable input parameters are also in close agreement with observations. The significance of agreements and discrepancies could be clarified using characterization measurements with finer depth resolution.