Earlier quoted context omitted.
They would just serve the paper using the usual techniques for delivering legal papers to persons possibly unwilling to receive them. These techniques usually avoid identifying yourself upfront. I believe they rather want information which they cannot legally force her to divulge (otherwise see above), so they're trying their luck at intimidation.
That isn't always true. In the U.S. legal system, a person can be granted immunity, and in doing so have their 5th amendment protection against self-incrimination terminated. With that, they could be forced to provide testimony, and refusal could result in fines and jail time without due process for as long as the courts see fit.
Jail time does seem appropriate for non-compliance with a legally binding judicial order (I'm not endorsing or condemning the existence of these laws, btw)