A coworker of mine ended up in a catch-22, and I don't remember how he resolved it. He needed to renew his driver's license, which required him to show his birth certificate. He had lost his birth certificate, so he needed to get a new copy, which required him to show his driver's license as ID.
As far as Superman and Ultra Woman go, I think they would need to approach ID issues as immigrants. They obviously wouldn't have US-issued birth certificates. They could claim that Krypton didn't issue birth certificates, or that they were destroyed with the planet. Making fake Kryptonian birth certificates seems risky to me.
How do immigrants or tourists get a marriage license? I guess someone who is here legally would have a passport they could use as id.
Alternatively, what if they have a "Kryptonian" ceremony? How does the government recognize foreign marriages? If SM and UW get married elsewhere, especially if it's in international waters and not in any country's jurisdiction, could they claim that they followed Kryptonian custom and therefore have a valid marriage? I could see Lois and Clark going this route, especially if they were already legally married in their civilian identities.
