No campground at Emerald Lake, but the Kicking Horse campground is only 16km away and is nice, I've stayed there a few times. It is all first come first serve.
Kicking Horse in Yoho was absolutely a peak experience and two and a half years ago when we visited, we had no trouble getting a campsite in late June. Just beautiful and close to Emerald Lake and there is another lake, similarly spectacular, but I don't remember the name.
If you're staying at Kicking Horse, don't miss the drive up to Takkakkaw Falls - paved, but no trailers. Came across a Moho stuck on a guard rail once... hope you're not going soon - a rock slide has the highway closed! Might want to double-check that it's still first come-first serve - quite a few of the National Park campgrounds are reservation only.