Experimentally Verifying a Clock's Accuracy So recently one of my professors went off on a tangent, and we ended up discussing atomic clocks and how they work, which is something I've always been fascinated with and thoroughly enjoyed.  But it left me with a question he couldn't answer.  
After you've built an atomic clock (or any clock for that matter), how do you verify that it is, in fact, working at a specified level of accuracy?
Let me be clear here.
I understand that by knowing the properties of the atoms and the lasers and all the other parts, you can calculate what frequency it should work at, but once it is working, how do you verify that it is working at that level, without needing a more accurate clock?
Once again, to be clear:
I'm NOT asking about how they build/design the clock.
I'm NOT asking about how they calculate the theoretical values.

I want to know how you can experimentally prove that a clock is working at its theoretical accuracy (or within an acceptable level of accuracy).
 A: This is an excellent question.  At the heart of it is this: you compare the clock to another copy of the same clock.  Well, actually you need to compare three identical clocks to each other to make a strong statement about the clock noise, but lets not worry about that for now.  If the noise of your clock is stationary (which it better be for a good clock), then the noise you measure will be given by
$$
S_t=\sqrt{S_1+S_2}=\sqrt{2}S_c,
$$
where $S_t$ is the total noise and $S_c$ is the noise of the identical clocks.  
On a technical note, you might be interested to know how one can compare two clocks.  The answer to this lies in the fact that clocks are just oscillators producing waves of some sort.  Some examples of devices which can be considered clocks are: mechanical oscillations of quartz crystals, atomic transition lines (in this sense a laser is a clock too), or the orbital period of a dead ultradense star.  Comparing two oscillators is as simple as summing the two waves.  This produces a beat note which tells you the difference in frequency between the two, i.e. the difference in timing between the two. 
An interferometer is very similar in this regard.  How do you measure a length much smaller than any ruler you have? You compare it to another length which is measured just as accurately.
A: That's a fundamental problem with all measurement devices.
What you can do is to compare your clock with other clocks. If yours differs significantly from the average then you know your clock is inaccurate.
Of course, this does not protect you from overall errors (i.e. a fundamental flaw in the mechanics/physics behind the device). 
A: Let's first recall that there is a strict definition for (how to determine) whether a given clock $A$ is "accurate" (or "good"); namely:
if for any three of its indications, $A_J$, $A_K$ and $A_Q$,
the durations of clock $A$ between pairs of those indications, say 
$\Delta \tau_A [ \small{\text{from }} A_J \small{\text{ until }} A_K ]$ and
$\Delta \tau_A [ \small{\text{from }} A_K \small{\text{ until }} A_Q ]$,
and the real numbers $t[ A_J ]$, $t[ A_K ]$ and $t[ A_Q ]$ which are associated to the clock indications as readings
satisfy the relation 
$$ \frac{(t[ A_K ] - t[ A_J ])}{(t[ A_Q ] - t[ A_K ])} == \frac{\Delta \tau_A [ \small{\text{from }} A_J \small{\text{ until }} A_K ]}{\Delta \tau_A [ \small{\text{from }} A_K \small{\text{ until }} A_Q ]} $$
then this clock $A$ is "accurate", or "good"; and otherwise it is not.
As far as the readings "$t$" are considered given (in the simple case of a "ticking" clock for instance as "the number of consecutive ticks" counted after a suitable "starting tick") and the left-hand-side of the equation is readily calculated, the remaining task is therefore to evaluate the ratio of durations on the right-hand-side. (In the described case of a "ticking" clock the question becomes "simply", whether this clock's duration from one (initial) "tick" indication to the next was and remained equal, for any initial "tick" indication; or how those durations varied.)
The short, perhaps superficial answer to your question is consequently that the accuracy of any given clock cannot be determined without comparison to a clock of known accuracy; ideally such as the "ideal clocks" considered by MTW §16.4. 
A more careful answer would not only present the constructions of various such "ideal clocks", but also discuss the assumptions (or "construction pieces") which they require, and whether they comply to Einstein's maxim (concerning experimental determinations) that 

All our well-substantiated space-time propositions amount to the determination of space-time coincidences [such as] encounters between two or more [... participants].

