That depends a lot on the specific numerical method in use, 2D/3D, and application.
Common reference problems are likely to have an analytical solution or be verifiable qualitatively by some fundamental principles.
I would bring up the common examples I use personally from each category:
Wave scattering from a perfect electric conductor (PEC)/dielectric/layered-coated sphere. This problem has an analytical solution (via Mie series) and can test multiple numerical aspects of the solver. Usually, a dipole or a planewave excitations are used.
Testing reciprocity (where it is applicable): doing two simulations interchanging the resultant sources and observed fields.
I also use application-specific benchmarks for power, microwave, antenna, electromagnetic compatibility (EMC).
Also, it is important to mention the method of manufactured solutions (MMS) with some relevant discussions here and here.