Do you still roll saves against effects suppressed by the Calm Emotions spell?


The Calm Emotions spell says:

…suppress any effect causing a target to be charmed or frightened. When this spell ends, any suppressed effect resumes, provided that its duration has not expired in the meantime.

On first read, it seems that the expiring duration would suggest waiting out a fixed time frame. However, a lot of fear effects permit saves throughout the duration to end them.

So two questions:

  1. While a fear effect is suppressed are saves still made to end it?
  2. If so, does a creature need to comply with special requirements to attempt the save while the effect is suppressed by Calm Emotions?

To clarify, this is the text for a Red Dragon’s Frightful Presence and the Fear spell, respectively:

Frightful Presence

Each creature of the dragon’s choice that is within 120 feet of the dragon and aware of it must succeed on a DC 19 Wisdom saving throw or become frightened for 1 minute. A creature can repeat the saving throw at the end of each of its turns, ending the effect on itself on a success. If a creature’s saving throw is successful or the effect ends for it, the creature is immune to the dragon’s Frightful Presence for the next 24 hours.

Fear

While frightened by this spell, a creature must take the Dash action and move away from you by the safest available route on each of its turns, unless there is nowhere to move. If the creature ends its turn in a location where it doesn’t have line of sight to you, the creature can make a Wisdom saving throw. On a successful save, the spell ends for that creature.