Umbran Watch

The Umbran Watch is a special type of watch that appears to be an object that most Umbra Witches possess. Both Bayonetta and Jeanne wear their watches on their chests.

In the first game, Bayonetta's watch contains a red jewel that is heavily implied to be one of the stones from the Eyes of the World. When she later meets Cereza, the girl also possesses a watch that is nearly identical except for the jewel.

Jeanne's watch is similar, it's silver and it doubles as a compact.

Bayonetta
In the first game, Bayonetta wears her Umbran watch on a small leather-like disc on her chest. Jeanne's watch is pinned to the large collar of her outfit.

Following the defeat of Iustitia, Cereza shows Bayonetta her own Umbran Watch after being asked if she possesses anything important to her. Intrigued, Bayonetta asks how Cereza obtained it; the young girl reveals that she received it as a birthday present from her mother. Hearing this, Bayonetta pulls a ribbon from her hair and ties it to the watch before putting it around Cereza's neck, telling her to never lose it and keep it close to her heart.

After defeating Father Balder near the conclusion of the game, Bayonetta uses her own Umbran Watch to access the time portal that Balder used to bring Cereza to the present. As she returns her younger self to her own time, Bayonetta reminds her to keep her "treasure" safe.

However, these actions prove to be the final step in Balder's true plan; after her adventures in the future, Cereza followed her future self's advice and wore the watch around her neck at all times. When Jeanne attempted to seal her away in order to prevent her from awakening as the Left Eye, the watch blocked the blow that would have initiated the ritual. Unable to be sealed away and with newfound confidence, Cereza decided to be strong like her "Mummy", joining Jeanne in battle against the forces of Paradiso. Upon realizing this in the present day, Bayonetta's memories are restored, awakening her as the Left Eye and allowing Balder to resurrect Jubileus.

Bayonetta 2
Despite changes in attire for the two witches, both Bayonetta and Jeanne continue to wear their Umbran Watches. Bayonetta now wears hers on a chain around her neck, still possessing the red gem though it's basically useless. Jeanne's watch is pinned to the right side of the chest on her new bodysuit.

It is revealed in Bayonetta 2 that the Umbran Watches that both Bayonetta and Jeanne wear is what keeps them from physically aging. This explains how they are both able to look the same as they did 500 years ago. When Jeanne is dragged to Inferno after a demon summoning gone wrong, Bayonetta uses Jeanne's watch to keep track of how much time is left, as she only has a day to rescue her friend before her soul is trapped forever.

Trivia

 * Both Bayonetta's and Jeanne's watches contain numbers in the demonic alphabet. Bayonetta's watch contains the numbers 14111219 and Jeanne's watch displays the numbers 141216. These numbers, according to character designer Mari Shimazaki, represents the year/month/date of both Witches' birthdays.
 * Lumen Sages also have their own version of the Umbran Watch called a Lumen Watch.