Not sure if women generally get different readings but I did a comparison of several body fat calculation methods using myself as the test subject a few years back.
Results:
Navy method: 4 measurements plus height and weight - 22.3%
Accu-measure method: skin fold calipers, one site - 17%
Tanita scale: non athlete mode - 25.5%, weight 141.8 lbs
Taylor scale: athlete mode - 15.9%, weight 140.4 lbs
Zone diet BF calculator: 2 measurements, height and weight, activity level - 24%
Picture comparison: looking at pictures of different female BF % - 20%
Bod pod test: weight 141.0 lbs, body fat 20.0%, lean mass 112.8 lbs
OK, my self estimation method results ranged from 15.9% to 25.5%, with the professionally done bod pod result of 20.0%. So as you can see, the best free method I found for accurately estimating BF% is just looking at pictures of women with known body fat percentages to see which one most closely resembled what I look like, or just taking the high and low estimates and averaging them.
I got a DEXA scan about a year ago, it said I was at 19.9% while my Garmin scale in athlete mode said I was around 23%. My home scale readings are always about 3% high in athlete mode, non athlete mode is about 6% high.