  We derive several upper bounds for the superfluid stiffness $D_s$ for Bose
and Fermi systems in terms of expectation values of local operators using
linear response theory and variational methods. These give insight into the
non-trivial dependence of $D_s$ on parameters such as disorder and interaction
in systems with broken continuous translational invariance. Our best
variational bound for disordered systems is obtained by allowing the phase
twist applied at the boundary to be distributed inhomogeneously within the
system. Path integral quantum Monte Carlo simulations are used to
quantitatively compare the bounds and $D_s$ for disordered interacting Bose
systems.
