How would I measure that I'm at a pole? How would a person measure that he is at a planetary pole? My first inclination is to use a sextant to ensure that the Sun remains at a constant inclination. However, due to the orbit around the Sun and a possible planetary axial tilt, the Sun's inclination may vary over the course of the year and that could affect measurements if the length of the day is a significant portion of the length of the year.

A second inclination is to try to identify a pole star or at least the point about which distant stars rotate during the course of a planetary rotation. The observer could then (at least in theory) measure the inclination of this point assuming that planetary precession takes a long enough time (as on Earth). However, in the most likely chance that there is no bright star near the pole, I don't see how a sextant could measure reliably the inclination of a blank point.

Perhaps the first method could be used, but with other objects in the sky (stars) in place of the Sun. Thus, if a given star's inclination does not change as it (apparently) revolves around the horizon, we are at the pole.

Are there any better methods, assuming a completely self-contained system (i.e. no external satellites)?
You could confirm with taking an image of the star trails.  They would form a circle with the apparent center at the zenith of the location.  You do not need a pole star at all.  Just a night of viewing.

You would also be able to tell based on the height above the horizon that the sun is.  On the equinox, the sun would be on the horizon at noon (when it is at its maximum height).  On the summer solstice, its angle will be above the horizon equal to the angle of precession.  And below by the same amount on the winter solstice.  

Measuring latitude using the sun

For any other day in the year, you will need to determine the max angle based where you are between the equinox and solstice.

Compensating for the Earth's tilt

Basically, you would determine if you were at a pole the same way you determine any other latitude.  You are just looking for a result of 90 degrees.