I did some work on using the AD5933 a few years ago. At first, I couldn't understand why the chip wasn't more commonly used in impedance measurement, but the more you look into it, the more annoying the drawbacks become. I wrote up some of my findings in my blog
(See here
http://electronicsdesigner.blogspot.co.uk/2011/04/design-for-precision-lcr-meter-part-2.html )
In order to get an acceptable frequency range, you really need an external oscillator with some method of selecting different clock frequencies. I went with a low-end DDS chip. Cheap to buy and easy to program with the same embedded micro you are using to talk to the 5933. I wouldn't run the drive oscillator faster than the design limit of 100kHz. As you have seen, at that point, you start to get components from other frequencies showing up, so you really need to filter the output, which of course adds its own phase+magnitude curve to be calibrated out.
Impedance range limitations: In order to measure the sort of inductors and capacitors a typical hobbyist may use, the 5933 is going to be outside it's normal measurement limits. Fine if you want to measure a 10K resistor, less so if you are measuring a 10pF capacitor. As you would expect, Analog Devices has some excellent application notes, and it is well worth digging around in them to see how they suggest increasing drive current, and improving sensitivity dynamic range etc. I ended up using an analogue multiplexer to select drive and receive gains via feedback resistors in the op-amps. I also included a small TrimDAC both to zero the offset, and induce a DC drive offset to investigate how capacitance changes with respect to voltage (3 years before Dave's video!)
As you can imagine, this changed a neat little solution into a bit of a Frankenstein's monster - although I must admit I thoroughly enjoyed doing it. After some thought, I realised I could probably just replace the AD5933 with an ADC and DAC driven straight from nice cheap fast ARM DMA ports. I wouldn't need the DDS then, and I would have much more control about how the measurement is made, and the processing done on it. Of course, you could just drive it directly from the DDS, way up into the RF regions, and simultaneously measure the current and voltage with much higher precision than the 5933 does.
I really should write up how it progressed, and the tests I did with it, but for the limited audience it doesn't really seem worth it, and it has mostly been cannibalised for other projects now. If I prototype a "new improved" direct measurement version, then I will definitely publish it with photos etc. I just need the enthusiasm! Like Dave and his uPower power supply design, you get to a point where you have done all the interesting stuff and it becomes hard work for little return.