  We study Wilson surface defects in 6d $\mathcal{N}=(2,0)$ superconformal
field theories, engineered by semi-infinite M2-branes intersecting M5-branes.
Two independent approaches are used to obtain the Wilson surface observables on
the $T^2$ inside Omega-deformed $\mathbf{R}^4 \times T^2$. One approach is to
compute 5d $\mathcal{N}=1^*$ instanton partition functions in the presence of
Wilson lines, where the instanton corrections capture the 6d Kaluza-Klein
momentum modes. The other approach is to study the elliptic genera of 2d
$\mathcal{N}=(0,4)$ gauge theories, which we propose as describing 6d self-dual
strings in the presence of Wilson surface defects. We make a detailed
comparison between these two independent computations, which precisely agree
for Wilson surfaces in minuscule representations; for non-minuscule
representations instead we only find partial agreement, due to technical
problems which we comment about.
