Usually, the same as it would for a contract for some non-currency commodity: by converting it to what it considers an equivalent value at the time of injury (not time of award or payment) in the legal tender currency.
That seems counter to the ethos of the BitCoin enthusiasts.
I also doubt it will necessarily work for large sums. Governments may enforce contracts related to foreign money (if they find that the contract itself is in their jurisdiction, which isn't always the case) because they have quid pro quo agreements with other states, and it is mutually beneficial to global trade if global contracts can be enforced. (In a way, it similar to foreign mail being carried by local postal services.) But there is no quid pro quo with any friendly BitCoin government, so there is no incentive to enforce contracts.
That's because it's a non-realistic ethos.
If you are a business, why would you ever try to run on bitcoin alone? There would have to be a huge advantage. And we see that in many small cottage industries where that is an advantage, like buying drugs online or illegal gambling.
But without the need for pseudo-anonymity why would anyone ever use it? Why would your grocery store use bitcoin over dollars? They wouldn't.
So crypto will probably be a currency in the long run, but it won't overthrow regular fiat.
Plus, if there was a huge benefit to crypto, the Fed could just do a crypto dollar and peg it to the real dollar.
To some extent yes, but for any more serious business this really isn't a problem at all. I've been running a business that makes income in bitcoin only for 5 years now, and converting for taxes and accounting is quite trivial actually. Hardly any work is spent on those problems. You know, that kind of stuff is very trivial to automatize using those computers, unlike many other problems.
Because the want the money from people which have bitcoins? Because creditcard fees are to high? (just forget about the BTC fees or the nearly fictional double spending problem) Another reason could be that the owner has Bitcoins and wants to support them. There might be more reasons.
Sure, if usage of that other currency is trivial enough volume that it doesn't threaten the government's currency. That's the sticking point. Bitcoin is allowed to exist at the whim of the government.
My government will enforce a contract even if it is denominated in some foreign currency, will it not? Currency used is independent of jurisdiction.
They may award damages in legal tender, rather than in Bitcoin, but I have to pay taxes in legal tender anyway, so there will always be a market to convert back.
Right now they might be confused by Bitcoin enough that they won't effectively be able to assess damages, but that's not necessarily a permanent state of affairs.