We present a numerical diagonalization study of two one-dimensional S=1/2 antiferromagnetic Heisenberg chains, having nearest-neighbor and Haldane-Shastry (1/r(2)) interactions, respectively. We have obtained the T=0 dynamical correlation function, S-alpha alpha(q,omega), for chains of length N=8-28. We have studied S-zz(q,omega) for the Heisenberg chain in zero field, and from finite-size scaling we have obtained a limiting behavior that for large omega deviates from the conjecture proposed earlier by Muller ct al. For both chains we describe the behavior of S-zz(q,omega) and S-xx(q,omega) for selected values of the applied held, and compare with previous work by Muller et al. and Talstra and Haldane. Suggestions for future finite-field neutron scattering experiments are made.