Methods to evaluate the quality of an IIR Filter fixed-point implementation
Any type of test result will be extremely dependent on the implementation, the filter coefficients and the actual input signal. Typically you would start with a detailed mathematical analysis of your filter implementation and calculate the transfer function from the input to each of the state variables. Based on either sine-wave scaling or "absolute sum of impulse response scaling" you can determine the max value of your states and determine the scaling that prevents clipping. The number of bits is then determined by your required SNR and how the noise propagates from the state variables to the output.

Next your check your rounding behavior: Safest is "round towards zero". That leaves a little of of SNR on the table, but it prevents any type of limit cycles. 

Finally you test it. You either construct the worst case signals and or create a set of test signals that covers anything that can happen in your application including some of the corner cases. Than, indeed, a simple "RMS error" metric is a good choice.