  Recently it was pointed out that transition frequencies in certain diatomic
molecules have an enhanced sensitivity to variations in the fine-structure
constant $\alpha$ and the proton-to-electron mass ratio $m_p/m_e$ due to a near
cancellation between the fine-structure and vibrational interval in a ground
electronic multiplet [V.~V.~Flambaum and M.~G.~Kozlov, Phys. Rev. Lett.~{\bf
99}, 150801 (2007)]. One such molecule possessing this favorable quality is
silicon monobromide. Here we take a closer examination of SiBr as a candidate
for detecting variations in $\alpha$ and $m_p/m_e$. We analyze the rovibronic
spectrum by employing the most accurate experimental data available in the
literature and perform \emph{ab initio} calculations to determine the precise
dependence of the spectrum on variations in $\alpha$. Furthermore, we calculate
the natural linewidths of the rovibronic levels, which place a fundamental
limit on the accuracy to which variations may be determined.
