What measures do celebrities take to protect their images from being used for commercial purposes without permission? How much does this typically cost them?

The Lanham Act - Federal. While the Lanham Act is generally thought of in the context of Trademark law, Section 43 has a provision regarding “false endorsement” that has been used by celebrities (notably, Carmen Electra) to fight the unauthorized commercial use of their likeness.

File a lawsuit and push for early settlement ($X,XXX to $XX,XXX+)

Take the lawsuit through trial ($XX,XXX to $X,XXX,XXX+)

Aaron Judge's 469-Foot Home Run in Kansas City Left Baseball World in Disbelief - Sports Illustrated

Right of Publicity Laws - Varies by state. Some states have statutes that specifically forbid using a celebrity’s likeness (and even voice) for commercial use without appropriate permission.

As far as the cost goes, that will vary depending on how far the celebrity has to go. Aside from the deterrent effect created by the mere existence of the laws (cost = $0), a celebrity may need to hire a lawyer to:

From a legal perspective, they rely on the various state and federal laws that give them actionable claims against people/businesses that use their images without permission. A few examples of these laws are:

Having read so much about Archie and Lilibet not actually existing, does anyone have any proof that they not only exist but that Meghan gave birth to them?

Common Law - Varies by state. Many states recognize what are known as “the four privacy torts,” which include “appropriation of another's name or likeness.”

Send off a Cease & Desist demand ($XXX to $X,XXX)