The impressive growth of wireless data networks has recently led to increased attention to the issue of electromagnetic pollution and the fulfillment of electromagnetic field (EMF) exposure limits. This paper tackles the problem of power control in user-centric cell-free massive multiple-input-multiple-output (CF-mMIMO) systems under EMF constraints. Specifically, the power allocation maximizing the minimum data rate across users is derived for both the uplink and the downlink. To solve such optimization problems, two approaches are proposed, i.e., model-based and data-driven. The proposed model-based solutions for the downlink utilize successive convex optimization and the log-sum-exp approximation for the minimum of a discrete set, whereas ordinary techniques are employed for the uplink. With regard to data-driven solutions, solutions based on both end-to-end architectures and deep unfolding techniques are explored. Extensive numerical results confirm that the proposed model-based solutions effectively fulfill the EMF constraints while ensuring very good performance; moreover, the results show that the proposed data-driven approaches can tightly approximate the performance of model-based solutions but with much lower computational complexity.