Return a null instead of throwing an exception and clearly document the possibility of a null return value in the API documentation. If the calling code doesn't honor the API and check for the null case, it will most probably result in some sort of "null pointer exception" anyway :)
In C++, I can think of 3 different flavors of setting up a method that finds an object.
Option A
Object *findObject(Key &key);
Return null when an object can't be found. Nice and simple. I'd go with this one. The alternative approaches below are for people who don't hate out-params.
Option B
void findObject(Key &key, Object &found);
Pass in a reference to variable that will be receiving the object. The method thrown an exception when an object can't be found. This convention is probably more suitable if it's not really expected for an object not to be found -- hence you throw an exception to signify that it's an unexpected case.
Option C
bool findObject(Key &key, Object &found);
The method returns false when an object can't be found. The advantage of this over option A is that you can check for the error case in one clear step:
if (!findObject(myKey, myObj)) { ...
