  Textbook quantum mechanics treats time as a classical parameter, and not as a
quantum observable with an associated Hermitian operator. For this reason, to
make sense of usual time-energy uncertainty relations such as $\Delta {t}\Delta
E\gtrsim\hbar$, the term $\Delta t$ must be interpreted as a time interval, and
not as a time measurement uncertainty due to quantum noise. However, quantum
clocks allow for a measurement of the "time at which an event happens" by
conditioning the system's evolution on an additional quantum degree of freedom.
Within this framework, we derive here two {\em true} uncertainty relations that
relate the uncertainty in the quantum measurement of the time at which a
quantum event happens on a system to its energy uncertainty.
