After some research, I believe I can answer my own question, even though it is a somewhat dissatisfying one.
There is no indication that progesterone supplementation helps prevent sporadic miscarriages (women have not had three or more pregnancy losses before).
However, in patients with three or more consecutive miscarriages immediately preceding their current pregnancy, empiric progestogen administration may be of some potential benefit.
There is currently a large study underway to test this effect, however, no results have been published yet.
edited a month later
The results of that large trial were published at the end of November 2015.
The study of 826 women with previously unexplained recurrent miscarriage showed that those who received progesterone treatment in early pregnancy were no less likely to miscarry than those who received a placebo (or dummy treatment). This was true whatever their age, ethnicity, medical history and pregnancy history.
From the study:
Progesterone therapy in the first trimester of pregnancy did not result in a significantly higher rate of live births among women with a history of unexplained recurrent miscarriages.
A Randomized Trial of Progesterone in Women with Recurrent Miscarriages
Sources and further reading:
Evidence-based management of recurrent miscarriages
Progestogen for preventing miscarriage (meta analysis of studies showing no impact on sporadic miscarriages, but effect for recurrent miscarriages)