  We present the theory for the effects of superconducting pairing fluctuations
on the nuclear spin-lattice relaxation rate, 1/T_1, and the NMR Knight shift
for layered superconductors in high magnetic fields. These results can be used
to clarify the origin of the pseudogap in high-T_c cuprates, which has been
attributed to spin fluctuations as well as pairing fluctuations. We present
theoretical results for s-wave and d-wave pairing fluctuations and show that
recent experiments in optimally doped YBa_2Cu_3O_{7-d} are described by d-wave
pairing fluctuations. In addition, we show that the orthorhombic distortion in
YBa_2Cu_3O_{7-d} accounts for an experimentally observed discrepancy between
1/T_1 obtained by NQR and NMR at low field. We propose an NMR experiment to
distinguish a fluctuating s-wave order parameter from a fluctuating strongly
anisotropic order parameter, which may be applied to the system
Nd_{2-x}Ce_xCuO_{4-d} and possibly other layered superconductors.
