I like using reaction torque sensor arrangements to measure the torque into "real" loads:
See, for example, this diagram from Futek's site. The commercial solutions like this tend to be pretty pricey, hundreds or thousands of dollars depending on the torque you need to measure. I've only priced out and purchased big ones, so I don't know about "servo" scale cost-wise.
For a cheap apparatus, you can mount the servo body on excellent low-friction bearings on-axis with the servo axle and restrain it from turning through a known lever arm and electronic scale (or a weight and string). I've built reaction-lever systems of this type around Flintec planar beam cells sold for weighing applications. These are relatively inexpensive and have good absolute calibrations. Of course, the bearings in this kind of setup contribute some error to your measurement that may be hard to characterize.
Your sensitivity requirements are quite stringent so you may have to experiment with measurement protocol and calibration no matter what you do. For a commercial torque cell, you can probably do a lot better than the nominal percentage accuracy (often something like 0.1% of full scale) but you'll have to do some work to trust the results.
You might build your own special apparatus that's "softer" than a normal torsion load cell or other reaction setup, so deflections at small torques are lower, but the performance of that will depend on the dynamics of your load. If the load varies, it could set up oscillations of a "soft" reaction torque device and the servo body.
Most reaction torque approaches won't lend themselves that well to integration into a tight space in an existing device, though.
Letting people know more constraints on your application would also be helpful. Can you freely modify the servo body mounting or not? Do you have ample space to install things, or are you trying to add this internally to a compact existing design?