Cu63 NMR shifts and spectra are presented for both Cu(1) and Cu(2) sites in a specimen of YBazCu3O6.64 (Tc60 K). For H along the c axis, the Cu(2) shift is not distinguishable from that reported for YBa2Cu3O7.0. For H in the a-b plane, the spin component of Cu(2) shift declines sharply as TTc. The Cu(1) shift behaves similarly, showing also a dramatic broadening at low temperatures in clearly nonmetallic behavior. Combined with anomalous T1 data reported earlier for the 60-K phase of YBa2Cu3O6+x, these results are shown to be consistent with strong and monotonically increasing antiferromagnetic correlations as T is decreased.