not sure whats the best technique, but i would like to point out that at note number C6 a step of +1cents will mean to differentiate between ~1000 and ~1000.5 Hz. in the realms of FFT this requires at least 128,000 bins.

if you used a strobe technique and wanted to tune to a reference frequency of A220 to within 1/10 cent the threshold beat frequency would be 0.0127 Hz, so to get an accurate reading you would need to sample a waveform that does not change frequency for 2/0.0127 seconds, which is 2 minutes and 39 seconds. At 48K Hz sample rate this is a window size of around 7,600,000 samples.

What are You trying to tune ? Any pitch to frequency whatever fiddle, sigmund, psy, yin and so on would output float as frequency. What matters is what to consider a stable period in sound which should be analysed. If You try to tune the guitar, it would need a while to settle down after the attack, strong tensioned string like on piano would behave better. Even a slight difference in pressure on guitar string would change pitch for several cents. Blow instruments would never make any sense to try to tune that precisely. Doing math arround deviation from perfect match to specific note, and converting that into fraction of a cent is not a big deal to do , question is what sense does it make to look at all the flying floats