Nuclear magnetic resonance (NMR/ON) measurements with beta- and gamma-ray detection have been performed on oriented Ag-104(g,m) nuclei with the NICOLE He-3-He-4 dilution refrigerator setup at ISOLDE/CERN. For Ag-104(g) (I-pi = 5(+)) the gamma-NMR/ON resonance signal was found at nu = 266.70(5) MHz. Combining this result with the known magnetic moment for this isotope, the magnetic hyperfine field of Ag impurities in an Fe host at low temperature (< 1 K) is found to be vertical bar B-hf(AgFe)vertical bar = 44.709(35) T. A detailed analysis of other relevant data available in the literature yields three more values for this hyperfine field. Averaging all four values yields a new and precise value for the hyperfine field of Ag in Fe; that is, vertical bar B-hf(AgFe)vertical bar = 44.692(30) T. For Ag-104(m) (I-pi = 2(+)), the anisotropy of the beta particles provided the NMR/ON resonance signal at nu = 627.7(4) MHz. Using the new value for the hyperfine field of Ag in Fe, this frequency corresponds to the magnetic moment mu(Ag-104m) = +3.691(3) mu(N), which is significantly more precise than previous results. The magnetic moments of the even-A Ag102 -110 isotopes are discussed in view of the competition between the (pi g(9/2))(7/2+)(-3)(nu d(5/2)nu g(7/2))(5/2+) and the (pi g(9/2))(9/2+)(-3)(nu d(5/2)nu g(7/2))(5/2+) configurations. The magnetic moments of the ground and isomeric states of Ag-104 can be explained by an almost complete mixing of these two configurations.