In general it's possible for electrons to jump to sub-orbitals which gives them a wider band of wavelengths that they can emit and absorb photons. The jumps between sub-orbitals are usually in microwave or radio bands.

Don't they usually create a photon with that energy?

For free atoms, yes. For atoms in a crystal lattice (or other solid), it's quite common for electrons to decay through phonon interactions, i.e. by emitting vibrations (i.e. heat) to the lattice.