We consider future balloon-borne and ground-based suborbital experiments designed to search for inflationary gravitational waves, and investigate the impact of residual foregrounds that remain in the estimated cosmic microwave background maps. This is achieved by propagating foreground modelling uncertainties from the component separation, under the assumption of a spatially uniform foreground frequency scaling, through to the power spectrum estimates, and up to measurement of the tensor to scalar ratio in the parameter estimation step. We characterize the error covariance due to subtracted foregrounds, and find it to be subdominant compared to instrumental noise and sample variance in our simulated data analysis. We model the unsubtracted residual foreground contribution using a two-parameter power law and show that marginalization over these foreground parameters is effective in accounting for a bias due to excess foreground power at low ell. We conclude that, at least in the suborbital experimental setups we have simulated, foreground errors may be modeled and propagated up to parameter estimation with only a slight degradation of the target sensitivity of these experiments derived neglecting the presence of the foregrounds.