  For electric quadrupole ($E2$) observables, which depend on the
large-distance tails of the nuclear wave function, ab initio no-core
configuration interaction (NCCI) calculations converge slowly, making
meaningful predictions challenging to obtain. Nonetheless, the calculated
values for different $E2$ matrix elements, particularly those involving levels
with closely-related structure (e.g., within the same rotational band) are
found to be robustly proportional. This observation suggests that a known value
for one observable may be used to determine the overall scale of $E2$
strengths, and thereby provide predictions for others. In particular, we
demonstrate that meaningful predictions for $E2$ transitions may be obtained by
calibration to the ground-state quadrupole moment. We test this approach for
well-measured low-lying $E2$ transitions in $^7$Li and $^9$Be, then provide
predictions for transitions in $^8$Li and $^9$Li. In particular, we address the
$2^+\rightarrow1^+$ transition in $^8$Li, for which the reported measured
strength exceeds ab initio Green's function Monte Carlo (GFMC) predictions by
over an order of magnitude.
