Once upon a time I was at a dinner at a computer science conference. At that time the existence of Chrome was a deeply guarded secret; I knew of it, but I was sworn to secrecy. Out of the blue, one of my dinner companions turned to me and asked "is Google working on a browser?"
This was a terrible dilemma. I could not answer "no" or "I don't know"; Christians mustn't lie. "Yes" would have betrayed my commitment. Refusing to answer would obviously amount to a positive answer, as would any obvious attempt to dodge the question ("hey I think that's Donald Knuth over there!").
I can't remember exactly what I said, but it was something evasive, and I remember feeling it was not satisfactory. I spent a lot of time later thinking about what I should have said, and what I should say or do if a similar situation arises again. Perhaps a good answer would have been: "aren't you asking the wrong person?" Alternatively, go for a high-commitment distraction, perhaps a cleverly triggered app that self-dials a phone call. "You're going into labour? I'll be right there!" (Note: not really, this would also be a deception.) It's worth being prepared.
One thing I really enjoyed about working at Mozilla was that we didn't have many secrets to keep. Most of the secrets I had to protect were about other companies. Minimizing one's secrecy burden generally seems like a good idea, although I can't eliminate it because it's often helpful to other people for them to be able to share secrets with me in confidence.
Update The situation for Christians has some nuance.