It would not be the energy left over but the effects of that energy. Since each weapon would be slightly different the spectrum/frequency/whatnot of its emitted beam/bolt/etc. would be slightly different and the effects of that energy on the area around the target (or where it passed through) could be detected and analyzed if one wanted to. Weapons such as lasers would have less of a issue with this since the beam's damage mechanism is pretty simple, but I imagine scaler weaponry would leave very distinctive traces.
Keep in mind this would only really be around the area it hit or, for very disruptive weapons (such as scalar and aether systems) the beam could very well cause secondary emissions (by interacting with particles on the way to the target and causing secondary emissions of radiation from them) that could leave a distinct trace in the material around the path (ground, trees, walls, etc.).
Chemically-propelled projectiles (cased and caseless weapons) would also leave chemical residue, though it would probably be more uniform between weapons of the same type (assuming the same amount of propellant and such).
In terms of a distinctive signature when fired, energy weapons would both have a advantage and disadvantage. They tend (I believe) to have less flash and other visible effects, but secondary radiation along the path (such as from ionized air) would be distinctively artificial in nature, whereas a subsonic, silenced projectile weapons emissions could fairly easily be attributed to natural phenomena (assuming they are not using something to see and track the round itself).