  We consider the prospects for measuring distinctive signatures of the
CP-violating phases in the minimal supersymmetric extension of the Standard
Model (MSSM) in light of the limits on sparticle masses from searches at the
LHC. We use the CPsuperH code to evaluate model predictions and scan the
parameter space using a geometric approach that maximizes CP-violating
observables subject to the current upper limits on electric dipole moments
(EDMs). We focus on the possible CP-violating asymmetry $A_{\rm CP}$ in $b \to
s \gamma$ decay and on a possible CP-violating contribution to the $B_s -
\overline{B}_s$ mass difference $\Delta M^{NP}_{B_s}$, as well as future
measurements of the EDMs of the proton, neutron and electron. We find that the
current LHC and EDM limits are consistent with values of $A_{\rm CP}$, $\Delta
M^{NP}_{B_s}$ and the proton EDM that are measurable with the Belle-II
detector, LHCb and a proposed measurement of the proton EDM using a storage
ring, respectively. Measurement of a non-zero proton EDM would constrain
$A_{\rm CP}$ significantly, but it and a CP-violating contribution to $\Delta
M^{NP}_{B_s}$ could still be measurable, along with neutron and electron EDMs.
A more accurate measurement of $A_{\rm CP}$ with the current central value
would favour stop and chargino masses within reach of future LHC runs as well
as a potentially measurable value of $\Delta M^{NP}_{B_s}$.
