  Monopole bubbling contributions to supersymmetric 't Hooft loops in 4d
$\mathcal{N}=2$ theories are computed by SQM indices. As recently argued, those
indices are hard to compute due to the presence of Coulomb vacua that are not
captured by standard localization techniques. We propose an algorithmic method
to compute the full bubbling contributions that circumvent this issue, by
considering SQM with more matter fields and isolating the bubbling terms as
residues in flavor fugacities. The enlarged SQMs are read from brane
configurations realizing the bubbling sector of a given 't Hooft loop. We apply
our technique to loop operators in $\mathcal{N}=2$ conformal SQCD theories. In
addition we embed this discussion in the larger setup of a 5d-4d system
interacting along a line, associated to the brane systems previously discussed.
The bubbling terms arise from residues of specific instanton sectors of 5d line
operators in this context.
