Is Kosher Cheese also Vegetarian (i.e. without animal rennet?)

If a cheese is listed as being Kosher, (for example on the igourmet.com website there is a whole section on kosher cheese), does that imply that any rennet in that cheese would have to be vegetable as opposed to animal derived? I'm a vegetarian, so must confess that I'm wondering this because it is is usually difficult to tell what kind of rennet is being used in cheeses, since it is most often simply listed as only "rennet." I've read that most rennets used in cheeses today are not animal derived, but I figure that if something can't be both labelled Kosher and contain animal derived rennet then my safest bet would be to seek out Kosher cheese. Thanks in advance for your help!