Upon occasion I have come across a plot line in a Regency historical novel where the couple is married by proxy. Unfortunately, such a marriage was not valid. Today’s interpretation of a marriage by proxy tells us that it is a wedding in which one (or both) of the people seeking to be married are not physically present and are being represented instead by another person. If both partners are absent a double proxy wedding occurs.
Nowadays, a proxy marriage might occur if one or both partners cannot attend for reasons such as military service, travel restrictions, imprisonment or when a couple lives in a jurisdiction in which they cannot legally marry.
Here is the U. S., four states deem proxy marriages as legal; those states are Texas, Kansas, Colorado, and Montana. Only Montana permits double-proxy marriages. A Federal Court in the U.S in 1924 upheld a proxy marriage of a Portuguese woman and a man living in Pennsylvania, where common-law marriages were legal at the time. Afterwards, the woman immigrated to the U.S., the marriage making her legal, whereas, before the marriage she would have been inadmissible due to being illiterate. In the early 1900s, Japanese “picture brides” arrived at Angel Island, California creating a significant increase in proxy marriages at the time. In the United States, if a proxy marriage has been performed in a state that legally allows it, many states will recognize it fully or will recognize it as a common law marriage. The exception to this is the state of Iowa where it is completely unrecognized.
Under English Common Law, if a proxy marriage is valid by the law of the place where the marriage took place (lex loci celebrations), then it is recognized in England and Wales. However, generally speaking, proxy weddings are not recognized as legally binding in most jurisdictions. There was no provision for marriages of English subjects in England by proxy marriage. Even before the Hardwick Marriage Act, a couple could be “half married,” meaning the betrothal, but they still required the ceremony in the Church of England to make their joining a fully valid marriage. The couple had to be present before the clergyman and swear to being there voluntarily before a marriage would be conducted.

A famous 17th-century painting by Peter Paul Rubens depicts the proxy marriage of Marie de’ Medici in 1600. By the end of the 19th century the practice had largely died out. Wikipedia
From the Middle Ages onward, European monarchs and nobility were sometimes known to by married by proxy. Some of those were
Mary, Queen of Hungary to Louis I, Duke of Orléans, 1385
Henry IV to Joanna of Navarre, the daughter of Charles d’Évreux, King of Navarre, 1402
Catherine of Aragon to Prince Arthur, 1499
Charles I of England to Henrietta Maria of Francy, 1625
Marie Antoinette to Louis-Auguste, 1770
Napoleon I of France to Austrian Archduchess Marie Louise, 1810
Other Recent Pieces on Proxy Marriage in the UK and the Laws in Place:
Immigration Inspector Warns of Rise of Proxy Marriage Misuse
Immigrants Using ‘Proxy’ Marriages to Dodge Britains Visa Laws
Migrants Win Right to Stay in UK with a Wedding They Don’t Even Turn Up For