Nuclear magnetic resonance on oriented nuclei was used in combination with beta-ray detection and ion implantation, leading to the successful observation of the resonance of (SrFe)-Sr-91. The magnetic hyperfine field (B-HF) was deduced as B-HF(SrFe)=-23.83(7) T using the known nuclear g factor. This result explains the existing problem of disagreement in B-HF values for SrFe between theory and experiment. An experimental nuclear spin-lattice relaxation rate was obtained and is briefly discussed in comparison with a theoretical estimate.