Detect Evil and Good
The spell detect evil and good will allow you to determine if a beast has a creature type consistent with a familiar:
For the duration, you know if there is an aberration, celestial, elemental, fey, fiend, or undead within 30 feet of you, as well as where the creature is located.
This works, since find familiar states:
Appearing in an unoccupied space within range, the familiar has the statistics of the chosen form, though it is a celestial, fey, or fiend (your choice) instead of a beast.
This won't explicitly tell you "this creature is a familiar", but if you know anything about familiars, you will know that a celestial, fiend, or fey appearing as a harmless beast will be rather suspicious; suspicious enough to say "this is probably a familiar".
Locate Animals or Plants
The spell locate animals or plants can tell us what need to know:
Describe or name a specific kind of beast or plant. Concentrating on the voice of nature in your surroundings, you learn the direction and distance to the closest creature or plant of that kind within 5 miles, if any are present.
With this one, if you suspect a nearby cat may be a familiar, cast this spell and concentrate on cats. If the suspicious cat pings with the spell, you know it isn't a familiar.
Channel Divinity: Arcane Abjuration/Abjure the Extraplanar (require a saving a throw)
These are conditioned on the suspected familiar failing a wisdom saving throw. The Arcana Cleric's Channel Divinity Arcane Abjuration says:
As an action, you present your holy symbol, and one celestial, elemental, fey, or fiend of your choice that is within 30 feet of you must make a Wisdom saving throw, provided that the creature can see or hear you. If the creature fails its saving throw, it is turned for 1 minute or until it takes any damage.
The Oath of the Watchers Paladin's Abjure the Extraplanar ability reads:
You can use your Channel Divinity to castigate unworldly beings. As an action, you present your holy symbol and each aberration, celestial, elemental, fey, or fiend within 30 feet of you that can hear you must make a Wisdom saving throw. On a failed save, the creature is turned for 1 minute or until it takes damage.
These aren't totally reliable, as they require a saving throw.
66% of the time, it works every time.
There are a few options for detecting fiends and celestials that do not detect fey. These include:
- The Paladin's Divine Sense feature.
- Helm of the Gods (from Mythic Odysseys of Theros)
Additionally, the Oath of Ancients Paladin's Turn the Faithless channel divinity turns a fiend or fey on a failed saving throw, but has no effect on celestials. The Oath of Devotion Paladin's Channel Divinity turns only fiends.