A similar question has been asked for Pathfinder, but I could not find any specific rules for 5e.
As an example, we have a Beast Master ranger with a wolf companion. The wolf has an added effect on its Bite attacks.
Bite. Melee Weapon Attack: +4 to hit, reach 5 ft., one target. Hit: 7 (2d4 + 2) piercing damage. If the target is a creature, it must succeed on a DC 11 Strength saving throw or be knocked prone.
For player characters, the DC for this type of effects is calculated as follows (example from the Ranger's Spellcasting feature):
Spell save DC = 8 + your proficiency bonus + your Wisdom modifier
When you select the Beast Master Archetype (PHB, p. 93) at level 3, your companion gains the following benefits of your proficiency:
Add your proficiency bonus to the beast’s AC, attack rolls, and damage rolls, as well as to any saving throws and skills it is proficient in.
Does this mean that the DC 11 Strength saving throw of the wolf's Bite attack increases with the proficiency bonus of the Ranger? Or is the DC of the bite attack for the wolf not actually calculated, but determined as a set value?