First, thanks to Rob for posting the actual text and to Sardathrion for the intelligent discussion of an option. But I respectfully disagree with both of them.
Bottom line
Since this wound up getting long, I added a section up front to just straight list my suggestion:
The ritual will make the character use a willpower point to resist any domination that would directly make them break the contract.
My default stance
The system explicitly says that the storyteller should use any means necessary to bring them into compliance. The storyteller always has license to do whatever crafts the best story even when it means overruling the rules, and this particular rule makes that even more explicit.
With that said, I look at the terms "unbreakable" and "into compliance" and I see this ritual mostly as one of compulsion. All signers must enter into agreement "voluntarily" (they have to actually sign, its not a ritual that can be done without some sort of consent, but nothing says it can't be signed under threat of torture or while the other party has a hostage...), but once entered the ritual has tremendous power over the signers to bring them into compliance.
So, I might use some poetic license in some cases, but for the most part I would view it as making the signers unable to take an action directly contrary to the contract, or fail to take a necessary action. They simply could not chose to break it. They could do things that would make fulfillment less likely to be possible (stalling on a contract with a deadline, for isntance) and that is where I would get more creative about making them slowly more uncomfortable.
But the ritual would compell them to do anything "within reason", and may provide punishment even for failing to do unreasonable things. What I mean is that if they expected to spend 3 nights fulfilling the contract, but it really takes three years, then they must spend 3 years working. But if they get to a situation where they have a chance of fulfilling the contract, but only by doing something clearly suicidal or by striking a deal with a demon, the ritual won't go so far as to make them die or give up their soul, but it will punish them for that kind of failure.
The ritual will not normally do something to help them comply. If they have a deadline, but they were bound in chains until it passed through no fault of their own, the ritual will not help them get out of the chains. They will struggle increasingly frantically as the deadline nears, using blood, disciplines, and anything else at their disposal but if they can't get out, they can't get out. Once the deadline passes, the ritual will punish them, but my "default" punishment is that they feel the need to make restitution to the other party commensurate with what the other party promised in the contract (which may be much less, or much more than what the bound up character promised.)
The way this would apply in the direct question is that the character being dominated to break the contract would be compelled to use a willpower point to help resist. But if the dominator overcomes that level of resistance, then the character reveals the secret.
At that point, the ritual has compelled the character to do everything within their power to try to uphold the contract. When they fail, the ritual will punish them, but my default punishment is restitution to the other party.
More creative options
That as I explained is my default. I would certainly feel free to do something a bit more creative, depending on circumstances.
For instance, if the dominating character did the dominating because the signer was subtly hinting that it was the only way for him to reveal that information and the signer was encouraging the domination, then the ritual will make him spend the willpower point and try to resist anyway, and then set his throat and mouth on fire to stop him from revealing it.
Of course, this is a contract, so verbiage matters. If the contract says he can't talk about it, he is free to write about it. If it says he can't reveal the information, then it might also set his hands on fire to stop him from writing.
I find having the contract grant bonuses possible, but a stretch. I view it as mostly about compulsion. The way I might work it is that if a character specifcally tries to invoke the contract then he can get a bonus, but he does so at a risk. For instance, if he is being dominated and deliberately invokes the contract he will roll int + occult (or some other related skill. Essentially I view it as him trying to consciously guide the power of the contract). Success means a bonus of 5 against that particular domination, and no punishment if the domination does force him to reveal. But failure means that the contract sets his eyes on fire to make the domination impossible.[Edit: Bob pointed out that might not work, so perhaps it sets his tongue on fire.] A botch means that the contract creates a massive inferno around him to make sure he can't be dominated and that he couldn't speak or write if his mind was somehow influenced.
Similarly, if he is chained up with a deadline ticking, the contract makes him fight and use blood points to fight harder. Invoking the contract successfully gives him a Potens boost to try to break the chains. Invoking it unsucessfully means he has to try to break his own bones or even chew his own body parts off to get out of the chains and the restitution will be multiplied if he still fails.
Why I think Rob and Sardathrion are reasonable, but wrong
Rob and Sardathrion have intelligent, reasonable answers, but I respectfully think they are both wrong. I think it is reasonable because the text says the storyteller should use discretion in enforcement, and also because there is an anology to real world contract law in "tortious interference with a contractual relationship". It lets the courts, under the right circumstances, "punish" someone who forces someone else to break a contract.
But I think it fails. For one thing, the analogy is imperfect. Tortious interference requires that the "interferer" have actual knoweldge of the contract, and that the interference is not somehow privileged. Although not technically a requirement, most successful cases of tortious intereference have some element of "wrongdoing". If I pay someone to break their contract with you and I did it primarily to hurt you, you can probably sue me successfully. If I pay someone to make my contract with them their top priority because I really need it done, then I am probably safe from a suit even if I fully knew that they had a contract with you and that fulfilling my contract would mean they probably couldn't fulfill yours. In this case, the dominator may not know about the contract and probably wants the information for its own sake, not just to make the character break the contract.
Second, this isn't law, it is magic. The magic has a certain scope, here it is the signers. It just doesn't have much influence on the world outside the signers. I know I just advocated letting it grant bonuses, but those are bonuses to the signer so the direct affect is still on the signer and the bonuses also came with risk attached to it if the signer chose to accept them. So, I think Sardathions idea of punishing the dominator directly is giving the ritual too much power. It is letting it affect those that didn't sign. At the very least, I think there needs to be a resisted roll between the ritual-caster and the interfer to see if the ritual can get any power over him, and even that seems a stretch to me.
Third, permitting Rob or Sardathrion's answer makes the ritual open to abuse. It seems clear that this is about making sure the other party complies. But I know it will help the other party comply I can use it to build in safegaurds. Say I know I want to succeed in something, but someone else with a strong dominate really wants me to stop. So, I contract with you that I will do my something and you will give me a dime. You hand me the dime immediately at the end of the contract so you have fulfilled your side and are safe. I can now go about my something knowing that I won't change my own mind, and no magical influence will change it for me. It might help me even more than that and let me break out of chains, etc.
Some GM's might call that creative spellcasting and allow it, but to me it seems really open to abuse (and there are other rituals that can be used to increase mental resistance anyway). Going with my suggestion of "invoking deliberately" does allow a certain amount of this, but it adds some pretty serious risks that will make people think twice about invoking, still focuses on compulsion, and its only direct effect is on the signers.
{Since I mentioned real world law, I will go ahead and say I am not a lawyer.}