A few years ago I was looking for a difficult cache with my partner, StudMcWilliams, on one of the many greenways of Raleigh. This particular cache was in a wooded area between the path and an apartment complex. As we trudging around the area looking under logs and in tree branches a curious onlooker came out of his apartment and asked us what we were doing. Stud said, "Looking for a cache." The man from the apartment, unaware of geocaching, answered back, "You're looking for your cat?" Without bothering to correct him, Stud said, "Yeah, that's right." Instead of leaving at that point, the man decided to be helpful and join the search. "What's it look like?" he asked. "It's small and grey," answered Stud, as these were the actual cache attributes. The search went on with the man's help for another 10 minutes until we ended with a DNF. "I hope you find your cat," he said as we parted ways. It occured to us later that if we had actually found the cache, it would have made an awkward situation even more awkward.
If some muggle happens to wander off the greenway and wonders what you're doing, just say: "I'm looking for 'My Lost Cat'." You won't be lieing.