What is the ruling on giving a female relative a decorated watch or mobile phone holder, with the expectation that she will use it for adornment in front of non-mahram men outside the home?

If the embellishments attract the attention of men, then it is not permissible to use them in front of non-mahram men, because a woman is commanded to conceal her adornment. Allah has forbidden believing women from striking their feet [on the ground] so as not to attract attention. If it is highly probable that your relative will adorn herself with it in front of non-mahram men, then gifting it is a sin, because it is an aid to sin. However, if it is not highly probable, then there is no objection. You must advise her by explaining the Sharia ruling and urge her to adhere to Allah's law.