For this answer, I turned to the member of our Wire Faculty who is an expert on ivory, "Scrimshaw" Mary Bailey.
On something that has been carved or cut, one should be able to see what we refer to as "checkering." Checkering is the natural growth pattern in the ivory, and not something that man can imitate by using plastics, resins or even ground-up ivory dust. Ivory also has a natural aging coloring process that takes place in it, and human body oils can enhance this change in coloration, especially in beads.
Usually, by tilting a carved piece at an angle, you will usually find evidence of this checkering in the ivory confirming that it is real and not imitation. Another method is a hot needle test. Heat a needle red-hot and touch it lightly to the ivory. If it is real, it will burn and stink something terrible! If it is imitation, it generally will melt and blacken like plastic does. (Ivory stinks like an overripe sewer when cut, and fossil ivory is worse!)
If you see any little pits in the material, it is probably a bone material of some type. Camel bone is one material used a lot to make beads out of and often mistaken for being ivory. Large backbone sections of fish can even be carved and can often be mistaken for ivory. Again, that pitted or pithy look is a dead giveaway that it isn't real.
P.S.: Wire-Sculpture does not, in any way, promote poaching or illegally-gotten jewelry supplies. None of our products contain true ivory. Many folks have heirloom ivory or finished ivory jewelry, and may be curious as to its authenticity, which is why we have provided a simple test.
Answer contributed by Dale "Cougar" Armstrong