In Unity there's a parameter for specularity (both modes) - Smoothness... I don't know what it corresponds to in Blender. You can bake two specularity maps: color and intensity, and at first I naively thought it to be intensity, but the result in Unity doesn't look quite right (beside the fact that it doesn't actually make sense). So I've decided that it's Hardness, but there's no baking option for Hardness in Blender, and I don't know what I'm supposed to do. I guess I could edit the alpha of the specular color texture down to prevent the object from looking like it's made from wet glass (although just the color is going to help there, I think), but maybe I'm missing something.
It doesn't really correspond to anything in Blender, unless you remake Unity's Standard Shader using Blender's Cycles.
The basic materials in Blender use relatively simply models, whereas Unity's Standard Shader is based on PBR and global illumination - where specular is much more complicated and interacts with a fresnel effect, in addition to receiving some light reflected by nearby surfaces. The Standard Shader material charts demonstrates what the different parameters mean. You may be able to get a better idea of how to accomplish what you're after by looking at those.
If after reviewing everything you're not actually interested in using full physically based rendering - which can be rather complex to bake for - you can simply switch the material to one of the Legacy Shaders in Unity.