Social scientists routinely rely on methods of interpolation to adjust available data to their research needs. This study calls attention to the potential for substantial error in efforts to harmonize data to constant boundaries using standard approaches to areal and population interpolation. We compare estimates from a standard source (the Longitudinal Tract Data Base) to true values calculated by re-aggregating original 2000 census microdata to 2010 tract areas. We then demonstrate an alternative approach that allows the re-aggregated values to be publicly disclosed, using “differential privacy” (DP) methods to inject random noise to protect confidentiality of the raw data. The DP estimates are considerably more accurate than the interpolated estimates. We also examine conditions under which interpolation is more susceptible to error. This study reveals cause for greater caution in the use of interpolated estimates from any source. Until and unless DP estimates can be publicly disclosed for a wide range of variables and years, research on neighborhood change should routinely examine data for signs of estimation error that may be substantial in a large share of tracts that experienced complex boundary changes.