This paper shows how to localize inside of a domain Ω dual norms of bounded linear functionals on the Sobolev space W^{1,p}_0(Ω). The only condition is that the functional in question vanishes over locally supported test functions from W^{1,p}_0(Ω) which form a partition of unity in Ω, apart from close to the boundary ∂Ω. The results allow in particular to establish local efficiency and robustness for a posteriori analysis of nonlinear partial differential equations in divergence form.