The find familiar spell description states:

When the familiar drops to 0 hit points, it disappears, leaving behind no physical form. It reappears after you cast this spell again.

While your familiar is within 100 feet of you, you can communicate with it telepathically. [...]

As an action, you can temporarily dismiss your familiar. It disappears into a pocket dimension where it awaits your summons. [...] As an action while it is temporarily dismissed, you can cause it to reappear in any unoccupied space within 30 feet of you.

The Ranger's Companion feature description for the Beast Master ranger has nothing suggesting any form of supernatural communication.

So if a familiar or companion dies away from the caster, on a scouting mission or something, is the caster aware?

There's no specific rules that cover it explicitly, so we'll have to rely on secondary techniques.

Familiar

The telepathy ability has a specified range - the character can easily go "Hey, are you dead?". No response tells the character the familiar is out of range, or dead.

Two actions allow the character to positively confirm dead-ness. Dismissing the familiar has no range limitation, so the caster can spend an action to dismiss the familiar and a second to recall it. If it doesn't respond to the recall order, deadness is confirmed. (Some DM's may allow it in one action by providing feedback on a "failed" attempt to dismiss.)

Ranger's Companion

You're on the money here - the beastmaster has no magical communication with his companion, and no ability to yank it back to him. He's out of luck, and doesn't have any short-term secondary method that would allow him to determine his animal's status. If the critter doesn't come back, he can spend eight hours and attempt to bond a new one - by strict RAW (the companion has to be dead) if it doesn't work, that tells him the original one is alive.