Space-borne remote sensing instruments measure high-dimensional vectors of radiances for each ground footprint over which they observe. These observations are converted into estimates of geophysical quantities through complex processing algorithms called retrievals. Many instruments use ``optimal estimation" (OE) methods based on Bayes' Theorem to obtain the posterior distribution of the state given the radiances, and report the estimated posterior mean and variance as a shorthand description of this distribution. However, numerous computational compromises and imperfect knowledge about other required inputs including the prior distribution, create uncertainties in these estimates. In this talk, we will describe a simulation-based approach to quantifying uncertainties in OE estimates of the posterior mean and variance that has been developed for NASA's Orbiting Carbon Observatory 2 (OCO-2) instrument. We will present results of our analysis, and discuss their implications for scientific conclusions drawn from OCO-2 data about the carbon cycle.