The examples in my J-E dictionary only use 秘める to hide something "within". IE, something intangible. The spirit within... etc. They actually use it for something like treasure, but again, this is on a far grander scale, and aren't necessarily related to something physical. You'll also not hear of someone using it in the every day sense, as with 隠す, which is something tangible. Car keys, remote control, or even another person.
My J-J dictionary (Daijirin) does say: 隠し人に知られないようにする。内緒にする。 But the examples, once again, are far more complex than what you would see with 隠す。
- 真相は長いこと秘められていた。
- 外には表れないが、内にもっている。
- 闘志を内に秘めた選手。
- 可能性を秘めている。
- 千年の歴史を秘めた杉並木。
Hope that helps.