We describe a general computational method for designing proteins that bind a surface patch of interest on a target macromolecule. Favorable interactions between disembodied amino acid residues and the target surface are identified and used to anchor de novo designed interfaces. The method was used to design proteins that bind a conserved surface patch on the stem of the influenza hemagglutinin (HA) from the 1918 H1N1 pandemic virus. After affinity maturation, two of the designed proteins, HB36 and HB80, bind H1 and H5 HAs with low nanomolar affinity. Further, HB80 inhibits the HA fusogenic conformational changes induced at low pH. The crystal structure of HB36 in complex with 1918/H1 HA revealed that the actual binding interface is nearly identical to that in the computational design model. Such designed binding proteins may be useful for both diagnostics and therapeutics.