D&D 5E - Keep Calm and Calm Emotions

Such is the weakness of natural language applied to a technical subject. I read it as, "For the duration, you can suppress any effect causing a target to be charmed or frightened" - you read it as, "You can suppress any effect causing a target to be charmed or frightened at the time of casting, for the duration." I would rule that emotions remained calm throughout the duration. Concentration is a heavy cost to pay and spells generally do not require it lightly. It also tells us that the caster is still connected to the spell effect.

I don't consider this a good analogy because that healing was instantaneous. Calm Emotions calms emotions for a duration (and requires active concentration from the caster on top of that).