I've heard that a dunk tank is the most accurate, but most of us don't have access to one. Short of that, I think that nine-site calipers consistently done by the same experienced (emphasis on experienced) person is the most accurate. Next best would be a three- or four-site caliper test, but why not go for all nine sites?
I'd say that bioelectrical impedance is next best, both handheld like the Omron and Tanita-type scales. They vary a lot during the day and depend on hydration. They also can give you different numbers depending on where you carry your fat. If you're bottom heavy, a Tanita scales will read high on you because it's sending its electrical current through your lower body, where a disproportionate amount of your fat is stored. Also, the algorithm they use is based on age and Mel and I can tell you that it reads BF very differently for someone who's 33 than someone who's 53. In fact, if I set my scale for 20 years younger, it's much more in line with a nine-site caliper reading. Does that mean I'm really 20 years younger??
They're good for tracking trends over time, but not real accurate for many people.
In my experience, the online sites that take your measurements and supposedly determine your body fat from them are pretty worthless. There really isn't any way to determine your body composition from your measurements. The tape measure can't tell if it's on top of fat or muscle.
One important thing to note is that no method is very reliable for someone who is obese. It's very difficult to caliper someone who is obese (though they are developing extra-wide calipers) and bioelectric impedance isn't very accurate either. I've read that someone needs to be in the high 30s to start getting accurate readings.
I think you can be pretty confident about the accuracy of your nine-site readings, Midwife.