sich vermählen
to marry
An elevated or old-fashioned term for getting married; to enter into marriage with each other.
Das Paar wird sich im Frühling auf einem alten Schloss vermählen.
The couple will marry in the spring at an old castle.

to marry / to unite
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to marry
An elevated or old-fashioned term for getting married; to enter into marriage with each other.
Das Paar wird sich im Frühling auf einem alten Schloss vermählen.
The couple will marry in the spring at an old castle.

'Vermählen' (to marry) belongs to the same word family as 'der Gemahl' (husband) and 'die Gemahlin' (wife). These words share an old root and all belong to an elevated, formal style of language.
Der Prinz und seine Gemahlin werden das Land regieren.
The prince and his wife will rule the country.
You can recognize the meaning of the word from the subject: if it refers to people, it means 'heiraten' (to marry). If it refers to things or concepts (e.g., aromas, styles, ideas), it means 'harmonisch verbinden' (to unite harmoniously).
Das königliche Paar wird sich im Sommer vermählen.
The royal couple will marry in the summer.
In the meaning 'heiraten' (to marry), 'sich vermählen' (to get married) is very formal, poetic, or even old-fashioned. In normal usage, 'heiraten' is almost always used.
In alten Romanen liest man oft, dass die Liebenden sich am Ende vermählen.
In old novels, you often read that the lovers marry at the end.
When referring to getting married, the verb is always used reflexively: 'sich vermählen' (to get married). It is often followed by the preposition 'mit' (with) to name the partner.
Sie hat sich mit ihrer Jugendliebe vermählt.
She married her childhood sweetheart.
to connect / to bandage
'verbinden' and 'vermählen' can both express that two different things are brought together. 'verbinden' is the normal, general word and fits in many situations. 'vermählen' sounds elevated, poetic, or artistic when it is not about marriage. It emphasizes that two things go together harmoniously or blend beautifully with each other. In everyday language, people usually say 'verbinden'. 'vermählen' is more suitable in texts about art, music, food, or style.

In diesem Gericht vermählen sich süße Birnen und kräftiger Käse zu einem besonderen Geschmack.
In this dish, sweet pears and strong cheese unite to create a special flavor.
Das Rezept verbindet frische Kräuter mit mildem Käse.
The recipe combines fresh herbs with mild cheese.