I am amongst those who thinks the anapanasati sutta suggests doing such contemplation after
the calming stages of the meditation. This is understandable, because a calm mind sees deeper and is more willing to let go of attachments & wrong ideas. Also, it may have had experiences of things disappearing that never disappeared before, like the willpower. This you can not contemplate without such experiences. So it's not a pondering, it's more a reflection, a contemplation of "what happened?"
So, I do contemplation after meditation, when the hindrances are weakened and mindfulness and clear comprehension/seeing (sati sampajanna) are strong. I think this is also how the Satipatthana sutta starts:
Herein (in this teaching) a monk lives contemplating the body in the body,ardent, clearly comprehending and mindful, having overcome, in this world, covetousness and grief; etc.
In fact, this comtemplation and the resulting understanding will come naturally if meditation was really deep.
"For a person whose mind is concentrated, there is no need for an act of will, 'May I know & see things as they actually are.' It is in the nature of things that a person whose mind is concentrated knows & sees things as they actually are.
However, we also find sutta references wherein investigation comes before calm. So this can also work. Calming and contemplation work together in this way too. However, I personally find this only really works if I already had some understanding through the practice I described above. Those insights I had before, can be recalled and serve as a base for calming the mind. This is not really an active contemplation, because it is just a recollection followed by immediately result. It does sometimes not even need thoughts.
But of course, there needs to be the mindfulness (recollection) deep enough to remember. When we are totally lost in emotions, this recollection will not come up or not work. When you are angry and try to convince yourself this anger is 'not-self', is not always the most fruitful way. The first atempt I would do is to practice metta as suggested in the MN20 sutta. Similar for other hindrances.
This basically describes the practice I've always been doing where calming and contemplating work together. Take what's useful and leave the rest. Also know that you can't force the understanding of the characteristics upon yourself. Some aspects are really deeply hidden, hard to see. So start where you are at.
Also, try some approaches to see what works. This is another part of starting where you are at. At times our approach may change a little. Here is a video of another kind of contemplation by Ajahn Jayasaro:http://www.youtube.com/watch?v=uqb7ZuMI8HY