  [abridged] Barack & Sago have recently computed the shift of the innermost
stable circular orbit (ISCO) due to the conservative self-force that arises
from the finite-mass of an orbiting test-particle. This is one of the first
concrete results of the self-force program, and provides an exact point of
comparison with approximate post-Newtonian (PN) computations of the ISCO. Here
this exact ISCO shift is compared with nearly all known PN-based methods. These
include both "nonresummed" and "resummed" approaches (the latter reproduce the
test-particle limit by construction). The best agreement with the exact result
is found from effective-one-body (EOB) calculations that are fit to numerical
relativity simulations. However, if one considers uncalibrated methods based
only on the currently known 3PN-order conservative dynamics, the best agreement
is found from the gauge-invariant ISCO condition of Blanchet and Iyer (2003).
This method reproduces the exact test-particle limit without any resummation. A
comparison of PN methods with the equal-mass ISCO is also performed. The
results of this study suggest that the EOB approach---while exactly
incorporating the conservative test-particle dynamics---does not (in the
absence of calibration) incorporate conservative self-force effects more
accurately than standard PN methods. I also consider how the conservative
self-force ISCO shift, combined with numerical relativity computations of the
ISCO, can be used to constrain our knowledge of (1) the EOB effective metric,
(2) phenomenological inspiral-merger-ringdown templates, and (3) 4PN and 5PN
order terms in the PN orbital energy. These constraints could help in
constructing better gravitational-wave templates. Lastly, I suggest a new
method to calibrate unknown PN-terms in inspiral templates using
numerical-relativity calculations.
