Wind-tunnel data of a grazing flow over porous wall-inserts to be used as a benchmark dataset for the development and validation of numerical modeling approaches of flows over and through porous media. The dataset contains several profiles along the streamwise extent of the wall-insert of the mean velocity magnitude, the turbulent intensity, and the turbulent length scale. Also included are some boundary-layer parameters of these profiles. These have been derived from single-component constant temperature hot-wire measurements. Additionally, the spectra of the unsteady wall-pressure fluctuations at several locations on the upper and lower surfaces of the porous wall-inserts are provided. These unsteady pressure measurements have been acquired using semi-infinite waveguide-type remote-microphone probes. Tested are two porous media with the same diamond-lattice pattern structure but different permeabilities and a reference solid-walled case. All three cases are tested at three inflow velocities: 15 m/s, 20 m/s, and 25 m/s. Modification in v3: Correction of permeability values in Table 1 on page 3 of AIAA_Manuscript_GrazingFlowPorousMaterials_v3.pdf.