Here is one way, perhaps MagWeb will come up with something easier =)
1) create a panel roughly the shape of where you want the honeycomb, that is thicker than whatever you want the honeycomb in. A good way to do this is to import a Plane, Select the relevant area on it, Smooth Boundary, delete the rest, and then Extrude it.
2) run Make Pattern on that. Use the default Tubes pattern. You might need to rotate the 3D gizmo 90 degrees, so that the tubes are going through the panel. This will create a honeycomb of holes
3) uncheck Clip To Surface, turn up the grid/mesh resolution a little bit, and set Reduce to 0. Then Update and Accept. This will create a bunch of little tubes that you are going to subtract from your object.
4) (optional) Add some resolution to the area you want to modify, so that the triangle size is in the ballpark of what the triangle size on the tubes is
5) select object, then shift-click on the tubes object, and run the Boolean Subtraction under Edits.
6) Wait a long time (depending on # of holes)
7) done! run Inspector to make sure there are no little glitches
If (6) fails, add more resolution to the area you want to modify. If the object you are subtracting from is very thin, this might not work, unless you add a ton of triangles. This video https://www.youtube.com/watch?v=RlgXiVMmoXk
might help you debug problems.