See Weyers et. al., Advances in the accuracy, stability, and reliability of
the PTB primary fountain clocks (2018). Here they report uncertainties on the PTB CSF2 Cs fountain clock at the $1.71\times 10^{-16}$ level.
In atomic clocks an electromagnetic oscillator (e.g. a laser beam or microwave tone) is made to interrogate an atomic transition. In this way the frequency of the electromagnetic oscillator can be compared to the frequency of the atomic transition.
The definition of the SI second is
The second, symbol s, is the SI unit of time. It is defined by taking the fixed numerical
value of the caesium frequency, ∆νCs, the unperturbed ground-state hyperfine
transition frequency of the caesium 133 atom, to be 9 192 631 770 when expressed in
the unit Hz, which is equal to s−1.
Now the Cs atoms in a real experiment do not exhibit an "unperturbed ground-state hyperfine transition". There are various systematic effects that shift these frequencies. But these systematic effects are studied so that they can be quantified and subtracted off. But the estimates of the systematic effects have uncertainty. This is why atomic clocks have finite uncertainty, despite the Cs hyperfine frequency literally being the definition of time.
In the linked reference, apparently the net uncertainty on these systematic effects was limited to $1.71 \times 10^{-16}$ fractional frequency uncertainty for CSF2.
We have
$$
9,192,631,770 \text{ Hz }\times 1.71 \times 10^{-16} \approx 1.57 \text{ }\mu\text{Hz}
$$
This means we can take this to mean that we can consider the atomic clock to be a measurement of the frequency of the microwave oscillator which yields a frequency measurement of
$$
9,192,631,770.0000000(16) \text{ Hz} \approx 9,192,631,770.000000(2) \text{ Hz}
$$
The proper way to express how precise this measurement is is using the fractional uncertainty reported as $1.71 \times 10^{-16}$. I don't like sig figs since they can lead to confusion, but nonetheless, printed this way we can see this measurement of the microwave oscillation frequency was performed with a precision of 16 significant figures.
I don't claim this to be the most precise measurement ever since optical atomic clocks have yielded much lower fractional uncertainties. But, unless the definition of the second is changed, those clocks suffer from a technicality that prevents us from printing out the result of their measurement as a unitful physical quantity with more than 16 significant figures.