They find the inspiration in something else. Usually these methods to get it are not right and decent: drinking alcohol, using drugs etc. Not very long ago actual women, wives or girl-friends, played a role of Muse for some artists. Today it is not necessary to an artist to have a Muse.
In ancient times three Muses were divine creatures and the daughters of Zeus. Their mother, Mnemosyne, was the goddess of memory. Hesiod decided to expand the number of muses, so now we know nine: Clio, Calliope, Euterpe, Terpsichore, Melpomene, Thalia, , Polyhymnia, Urania, Erato. Nine Muses were given different roles later by Romans: Clio was the muse of history, Erato of lyric poetry, Polyhymnia of sacred poetry and so on.
Nine muses were considered to be kind, caring creatures. According to Hesiod, they came to the chosen and lucky artist and presented him with their invaluable gifts. At the same time Muses could punish artists and other creatures. We all know how they punished Sirens when they want to compete with them: they made them loose their wings and Sirens fell into the sea.
The power of the ancient Muses was transferred to the modern ones. Many modern Muses were mostly strong women with difficult characters and interesting lives. Among them we can define Gala, the Muse of Salvador Dali, Georgia O’Keeffe, the Muse of Alfred Stieglitz, and many other. In the 21st century it is not very easy to find a Muse. Some artists still have Muses, very often they are their own wives, but the relationships between them does not have an element of divinity any more. They are just partners and their relations are the relations between two people, just human beings, usually with equal talent. Women do not limit themselves to the role of Muses any more, they want to create masterpieces themselves. Feminist ideas do not allow to treat women as objects.
Muses did not completely disappear, just the idea of them was changed.