  We construct equilibrium models of compact stars using a realistic equation
of state and obtain the density range occupied by the proton superconductor in
strong $B$-fields. We do so by combining the density profiles of our models
with microscopic calculations of proton pairing gaps and the critical unpairing
field $H_{c2}$ above which the proton type-II superconductivity is destroyed.
We find that magnetars with interior homogeneous field within the range $0.1
\le B_{16}\le 2$, where $B_{16} = B/10^{16}$ G, are partially superconducting,
whereas those with $B_{16} > 2$ are void of superconductivity. We briefly
discuss the neutrino emissivity and superfluid dynamics of magnetars in the
light of their (non)-superconductivity.
