  We construct solutions to the nonlinear magnetic Schr\"odinger equation $$
  \left\{ \begin{aligned}
  - \varepsilon^2 \Delta_{A/\varepsilon^2} u + V u &= \lvert u\rvert^{p-2} u &
&\text{in}\ \Omega,\\ u &= 0 & &\text{on}\ \partial\Omega,
  \end{aligned}
  \right. $$ in the semiclassical r\'egime with strong magnetic fields. In
contrast with the well-studied mild magnetic field r\'egime, the limiting
energy depends on the magnetic field allowing to recover the Lorentz force in
the semi-classical limit. Our solutions concentrate around global or local
minima of a limiting energy that depends on the electric potential and the
magnetic field. The results cover unbounded domains, fast-decaying electric
potential and unbounded electromagnetic fields. The construction is variational
and is based on an asymptotic analysis of solutions to a penalized problem in
the spirit of M. del Pino and P. Felmer.
