For a harmonic oscillator in one dimension, there is an uncertainty relation between the number of quanta $n$ and the phase of the oscillation $\phi$. There are all kinds of technical complications arising from the fact that $\phi$ can't be made into a single-valued and continuous operator (Carruthers 1968), but roughly speaking, you can write an uncertainty relation like this:
$\Delta n \Delta \phi \ge 1$
The fact that the right-hand side is 1 rather than $\hbar$ is not just from using natural units such that $\hbar=1$; we can see this because $n$ and $\phi$ are both unitless. This suggests that this uncertainty relation is a classical one, like the time-frequency uncertainty relation that is the reason for referring to data transmission speeds in terms of bandwidth.
However, the only physical interpretation I know of seems purely quantum-mechanical (Peierls 1979):
[...] any device capable of measuring the field, including its phase, must be capable of altering the number of quanta by an indeterminate amount
If this uncertainty relation is classical, what is its classical interpretation? If it's not classical, then why doesn't the restriction vanish in the limit $\hbar\rightarrow0$?
Carruthers and Nieto, "Phase and Angle Variables in Quantum Mechanics," Rev Mod Phys 40 (1968) 411 -- can be found online by googling
Peierls, Surprises in theoretical physics, 1979