What do you mean by result table? The Near tool does not generate a new table. It adds fields to the table of the input features with a near FID and near distance. Are you looking there for the results?
Are you specifying a Search Radius? If your search radius is smaller than the actual distance between features, it will not be recorded. Leaving the search radius blank will ensure that you capture the nearest feature regardless of distance.
I have tried both the "near" tool, which doesn´t generate a new table and the "generate near table" which creates a new tabel. When I use the near tool, all the new fields come with the same value: "-1". When I use the "generate near tabel" the table comes out empty. Both shapefiles and the dataframe are in projected coordinate system: UTM SAd 69.
I kept trying to change settings in the "generate near table" tool, and it worked when I unchecked the "Find only closest feature" option, wich is the default.