We study the order parameter phase fluctuation effects in cuprate supercond
uctors near T = 0, using a quasi-two-dimensional cf-wave BCS model. An effe
ctive phason theory is obtained which is used to estimate the strength of t
he fluctuations, the fluctuation correction to the in-plane penetration dep
th, and the pair-field susceptibility. We find that, while the phase fluctu
ation effects are difficult to observe in the renormalization of the superf
luid phase stiffness, they may be observed in a pair tunneling experiment w
hich measures the pair-field susceptibility.