I decided to try baking lighting with materials having specular maps and ended up with some weirdness. Either whole mesh was of some muddy color or it didn’t have any specular highlights.
Does UE4 support specular maps in materials made for static baked lighting or does it only support diffuse/normal maps?
Thanks
You need to use Reflection Captures to have specular from static lighting.
Some specular information is baked with light mass, mostly directional information when using stationary lights.
Also with the PBR materials UE4 uses, most materials should not need a specular texture or anything plugged into that slot. It’s mostly there for legacy reasons and leaving it empty is the most physically accurate option.
Doesn’t seem to work on mobile (ES2). Works in the Editor / PIE in SM5 preview, but not in ES2 
I wonder if it just doesn’t work with ES2 renderer or if I need to have HDR on in order for roughness to work on mobile…
Stationary lights do not actually bake any specular information, they bake a shadow mask which the stationary light uses in order to do realtime lighting. Basically like shadow buffering that doesn’t update every frame. That is why you can change their color and intensity without baking.
Can’t really use stationary lights, only static (all baked, nothing real-time).
I figured what the issue was - I forced fully rough and non-metallic in my project settings. So changing and tweaking materials didn’t have any effect.