We derive stability estimates in H2 for elliptic problems with impedance boundary conditions that are uniform with respect to the impedance coefficient. Such estimates are of importance to establish sharp error estimates for finite element discretizations of contact impedance and high-frequency Helmholtz problems. Though stability in H2 is easily obtained by employing a "bootstrap" argument and well-established result for the corresponding Neumann problem, this strategy leads to a stability constant that increases with the impedance coefficient. Here, we propose alternative proofs to derive sharp and uniform stability constants for domains that are convex or smooth.