  We calculate the spin stiffness $\rho_s$ for the frustrated
spin-$\frac{1}{2}$ Heisenberg antiferromagnet on a square lattice by exact
diagonalizations on finite clusters of up to $36$ sites followed by
extrapolations to the thermodynamic limit. For the non-frustrated case, we find
that $\rho_s = (0.183\pm 0.003)J_1$, in excellent agreement with the best
results obtained by other means. Turning on frustration, the extrapolated
stiffness vanishes for $0.4 \lesssim J_2/J_1 \lesssim 0.6$. In this
intermediate region, the finite-size scaling works poorly -- an additional sign
that their is neither N\'eel nor collinear magnetic order. Using a hydrodynamic
relation, and previous results for the transverse susceptibility, we also
estimate the spin-wave velocity in the N\'eel-ordered region.
