At Arc Desktop 10.7.1, this works for me (note that it requires the Spatial Analyst extension):
Open the Raster Calculator and enter the following in the Map Algebra Expression pane:
Con("your_raster" == "your_raster".maximum, "your_raster")
[Note: this selects the cell with the maximum value from your_raster.]
Enter the name of the output raster that ...