Step 1: Concept
Electromagnetic (EM) waves consist of oscillating electric and magnetic fields and travel at the speed of light.
Step 2: Analysis
X-rays, $\gamma$-rays, and microwaves are all part of the EM spectrum. $\beta$-rays, however, are fast-moving electrons or positrons.
Step 3: Conclusion
$\beta$-rays are particulate radiation, not electromagnetic waves.
Final Answer: (C)