Dual-energy X-ray absorptiometry (DXA) or X-rays are the most effective approach. But this exposes you to harmful X-rays. Technicians need to be highly trained. Equipment and the procedure are expensive. Unless a good physician tell you to do this, and it resonates well with your intuition, do not do it. Your body fat percentage can change in a day, anyway.
Interestingly, using this as the gold standard, this is the sequence from greatest to least, of accurate body fat percentage readings*: body pod (may explain in another blog), caliper measures, BMI and impedance. I worked at a gym about 10 years ago where they used impedance as progress over calipers. That did not land well with me. Well, I am right again. :)
*Sardinha LB, Lohman TG, Teixeira PJ, Guedes DP, Going SB. American Journal of Clinical Nutrition 68 (1998); 786-793.
My third book, Pocket Guide to Fitness, is available on http://www.authorhouse.com and http://www.amazon.com. If you look up my name on those Web sites, you will find my other books The Boy in a Wheelchair and Life, Work and Play: Poems and Short Stories. These two books are on my Web site http://www.louizapatsis.com.