The Zone of Truth spell contains the following clause:

You know whether each creature succeeds or fails on its saving throw.

In a scenario of checking someone's loyalty, any countermeasure that allows you to always succeed your save against this spell will alert the caster that you have succeeded the save. They will keep you in the area of the spell until you succeed, or until it's clear something is stopping you from failing - at which point the caster will tell you to remove whatever that effect is doing this, or have it assumed you are disloyal.

What are all the countermeasures to this spell which:

1. don't allow the spell to affect you, and


2. don't alert the caster you're unaffected?

Note that to fulfil (1), answers should avoid "you can lie by telling the truth in a ZoT". A competent interrogator will simply ask direct yes/no questions and assume disloyalty if they are not answered directly.

Mechanically, Zone of Truth can be defeated only by high-level features

As you say, any attempt to resist or evade the effects of Zone of Truth alerts the caster. And in the context of a loyalty test, avoiding the effect is synonymous with admitting disloyalty. The only exceptions to this are a handful of high-level features: the Mastermind Rogue's Soul of Deceit feature (as mentioned in Louis Wasserman's answer) defeats truth-detection magic, and the 8th level spell Glibness provides a similar ability:

[...] no matter what you say, magic that would determine if you are telling the truth indicates that you are being truthful.

Note that while Glibness causes Zone of Truth to read whatever you say as truthful, it doesn't necessarily protect you from being forced to tell the truth. If you intend to use it, you should ask your DM ahead of time how it will work with Zone of Truth to avoid arguments when it actually happens. (In contrast, Soul of Deceit explicitly says you can't be forced to tell the truth by magic, so there is no ambiguity there.)

In any case, unless you have access to features or spells available around 15th-17th level, you'll have to make it through your loyalty test by telling what your character believes to be the truth.

Believe your lies

However, there is at least one small and difficult-to-exploit loophole that doesn't require any powerful abilities: Zone of Truth only prevents a creature from speaking a deliberate lie. If you can manage to believe your lies, you will be able to speak those lies while under the effect of Zone of Truth. For example, if the loyalty question is something like "Are you loyal to the Empire?", then you would be able to answer with a simple "yes" even if you were plotting to assassinate the emperor, as long as you truly and honestly believed that doing so would help the Empire. Obviously, this is a very situational workaround, but I want to emphasize that this is materially different from being evasive or "lying with the truth". This is a case where you give exactly the truthful answer that is expected of you, but for a completely different reason (while praying that you are never asked to elaborate on that reason).

In practice, when you as a player attempt to use this, you should probably expect some push-back from your DM, asking if your character really believes this. This "loophole" has a heavy character focus rather than a mechanical focus, so if you are planning to do this, be prepared with a solidly fleshed-out backstory to justify your honesty. And of course, be willing to accept that a slightly different question might reveal that your interpretation of loyalty differs from that of your interrogators. In the above example, you would not fare well if you were instead asked "Are you loyal to the emperor?"

Unfortunately, I don't have any experience to share of using this "loophole" in an actual game. I'm just pointing out that it's the only loophole I can think of.

The Mastermind archetype for the Rogue class from Xanathar's Guide to Everything has a class feature, Soul of Deceit, which is explicitly about defeating truth magic: it says that you can't be compelled to tell the truth by magic and that magic that determines if you're telling the truth says you are.

This isn't succeeding on the save; it doesn't say anything about a saving throw. I would read the effects as that you make the saving throw as normal, but can ignore the results and lie as you like.

Modify Memory

Depending on the circumstances and the precise information you need to keep secret, you may able to effectively defeat a Zone of Truth by having your memory modified in advance by an ally using the Modify Memory spell. Affected creatures in a Zone of Truth cannot deliberately lie, but that doesn't mean that whatever they believe to be true actually is. After interrogation, someone surreptitiously casts Remove Curse or Greater Restoration on you and your original memory returns, at which point you presumably mutter "keikaku¹ doori".

Given the restrictions of Modify Memory this works best for concealing knowledge of specific events; the longer ago the events are or the more material you have to cover, the technique swiftly becomes impractical.

This doesn't strictly meet your constraints since it requires you to actually be affected by Zone of Truth and does not conceal that from the caster, but I am not sure there actually is a reliable way to render oneself immune to the spell without tipping off or having to compromise the caster. Either they know you're passing your saves, or by lack of information they know you're not even making saves and therefore aren't affected.

_{1. keikaku means plan}

Minor Illusion

You say yes, they hear no. You told the truth, but defeated the Zone of Truth with a cantrip.

If you need more certainty of success, just go with a higher level illusion spell.

Of course, you will need a way to cast it without detection, but I'm sure you can come up with ways given enough prep time.

Get Dominated

So you cannot speak a deliberate lie?

deliberate, adj. done consciously and intentionally

If you are not in control of your own actions, you cannot lie deliberately. You are forced to say what you say. Get an ally (standing outside the spell radius if possible to make sure) to cast dominate person on you and

take total and precise control of the target. [..] the
creature takes only the actions you choose, and doesn't
do anything that you don't allow it to do. (PHB 235)

You will still roll the saves against the zone of truth and the results will be known by the caster. It is just that this makes no difference regarding what you actually say.