To grossly oversimplify, astrobiologists generally consider three broad prerequisites for life:
- a liquid solvent (such as water)
- chemical building blocks (such as organic molecules)
- an energy source (such as sunlight, directly as in plants or indirectly as in animals who eat plants or eat other animals that eat plants)
Because water-based, carbon-based life fueled by stellar energy is what we know most about, this is generally what we look for. However, scientists do consider other configurations:
Though more exotic solvents (like ammonia, liquid nitrogen, or supercritical carbon dioxide) may exist in extrasolar systems, the only surface liquids outside of Earth that we know about today occur on Saturn’s smoggy moon Titan.
Titan's seas are made of liquid methane and ethane, which is considered as a possible alternative solvent for life.
Since we've never found life that uses a different solvent or building blocks (even on Earth), it is mostly hypothetical, and so we are limited in how much we can search for them. If we assumed that some sort of electromagnetic-based life existed, how would we go about looking for it? What are the signs that such life is present? We don't even know if such life is present on Earth.
Life, Jim, but Not as We Know It: Prospects for Life in Titan's Hydrocarbon Seas - NASA Astrobiology Institute