Building-Stock Energy Models (BSEMs) have grown in popularity, implementation, scale and complexity. Yet, BSEM quality assurance processes have lagged behind. This article proposes a scalable methodology to apply Uncertainty (UA) and Sensitivity Analysis (SA) to BSEMs and studies the performance of eleven common UA-SA methods (OAT, SRC, SRRC, FFD, Morris, Sobol', eFAST, FAST-RBD, DMIM, PAWN, DGSM) for three UA-SA targets: screening, ranking and indices. Applying UA and SA to BSEMs requires a two-step input parameter sampling that samples 'across stocks' and 'within stocks'. To make efficient use of computational resources, practitioners should (i) distinguish between three UA-SA targets and (ii) choose a method based on the aimed UA-SA target. The computational cost varies according to the UA-SA target and method; (i) for screening: OAT, SRC, SRRC, FFD and Morris; (ii) for ranking: SRC, SRRC and Morris and (iii) for indices: Sobol' is the most efficient, among the tested UA-SA methods.