How would a contemporary Jacobean audience view Shakespeare's presentation of marriage in The Tempest?
You should also consider the purpose of marriage as a structural device in the Comedies of Shakespeare's day. Though The Tempest does not conform to a traditional Comedy (We generally call it a Romance play.), the relationship between Ferdinand and Miranda was straight out of any Comedy written by Shakespeare, which means it begins with two young lovers who are "prevented" from being together (Prospero pretends to dislike and suspect Ferdinand), but who end up marrying.
The ending in at least one marriage was a traditional aspect of a Comedy in Shakespeare's day, not whether the script was "funny" or not. Lovers who want to be together, but are prevented from being together by obstacles (internal or external) was a huge aspect of comic plot structure for Shakespeare.
Interestingly, in The Tempest, Ferdinand and Miranda are both manipulated to "fall in love" with each other and prevented from being together (at least initially) by Prospero. He serves both as the creator of the comic structure (The two young lovers fall in love.), and the character in the story (A father who does not "approve" of his daughter's choice.) who stands as the obstacle to the fulfillment of that structure. Shakespeare seems to be commenting on this dramatic structure, one that the audience would have known well from other Comedies of the time.
It should also be noted that Shakespeare often played with the question of whose "choice" marriage is and/or should be. Marriage was definitely still an institution of arranged matches for the most part, but the Jacobean world was a changing one, and marrying for love and the idea of finding one's true love was on the immediate cultural horizon, and certainly a question that Shakespeare's audience entertained.
For more on Jacobean drama and love in Shakespeare's plays, please follow the links below.
We need to remember that marriage was a very different institution and phenomenon in the time of Shakespeare than it is today. During this time, the only possible career open to women was to marry and then to help their husband in running the household and assisting their husband in his profession. Likewise, as we can see in other plays, a woman was not expected to "choose" her husband. Marrying was a very important social obligation which allowed the family of the bride to make alliances, gain wealth and cement important social connections. We can see this in Romeo and Juliet when Capulet violently insists that his daughter marry Paris, and also in A Midsummer Night's Dream, when Hermia has no choice at the beginning of the play but to become a nun, die or fulfil her father's wishes and marry Demetrius.
When we think of The Tempest, therefore, depending on how we wish to stage this play, we can certainly see some of these elements in play. Consider how Prospero effectively manipulates the situation not just for his prisoners, but also equally for his daughter, and we could argue that there are elements of his speech where he displays a tyrannical, despotic nature towards his daughter:
Come on, obey!
Thy nerves are in their infancy again
And have no vigour in them.
The audience of Shakespeare's times would have seen nothing wrong or questionable in the way that Prospero creates a situation for his daughter to fall in love with Ferdinand. In fact, they would not have thought it necessary for her to fall in love with him at all. As Prospero's daughter, she should obey the commands of her father, whatever the feelings of her heart.