The way to measure chromatic tuners' precision
Precision and accuracy are 2 different things. 

1 cent is 1/100th of the frequency difference between 2 adjacent semitone pitches in equal temperament tuning.  The frequency ratio is exp(ln(2)/1200) or roughly 1.00059  

Precision of 1 cent might mean the tuner reports frequency error from the nearest semitone in 1 cent units, whether accurate or not.

To test accuracy, you might want to synthesize test signals that "sound like" your desired instrument (in software, or using a calibrated programmable synthesizer).  Feed those test signal to your tuner (or your tuner's pitch estimation algorithm in a software environment as unit testing).  If the results matches the synthesized pitch to within 0.5 cents, then your accuracy is 1 cent at that frequency.  Vary the test signal (perhaps randomized) to different semitone notes and cent (or cent fraction) offsets over your tuners entire range to find the worst case to evaluate (get a statistical estimate of) your tuners accuracy.

You can add Gaussian random white noise or recorded typical background room noises to your generated test signals to test measurement precision (repeatability) at realistic S/N ratios as well.

One "gold standard" is to measure the WWV audio frequencies (500 and 600 Hz), and use those to calibrate your synth and test your tuner.