No capacitor is ideal (i.e. infinite resistance). Depending on what type of capacitor it is, I can imagine various real, non-infinite resistance values. There is always resistance in parallel with the ideal capacity (insulators are imperfect) and a series resistance due to the leads. Can't avoid these.
If you are using an LCR meter to make this measurement, you have to remember it only really measures |Z| and theta. So if you get a bizarro value (e.g. negative resistance or capacitance) it's often because everything else is model and algebra dependent extrapolating from |Z|-theta raw data. Garbage-In-Garbage-Out.
Having such a large variance sounds like a noise/ranging/resolution problem. What instrument are you using to measure this? If you are using something like an HP/Agilent 4284A, it should have no problem with measure device values range but you'd need to autorange. Also: did you compensate your test fixture/cables? That can mess things up also. I'd also look at the raw |Z|-theta data first (this is how you can find bad compensation) and check your bias/osc levels (if your device is small, you may need more AC bias level, or less DC bias - if your LCR supports that).