As happens to young couples in most of Shakespeare's comedies, and in one notable tragedy, Romeo and Juliet, Ferdinand and Miranda fall deeply in love at first sight in The Tempest.

Miranda sees Ferdinand from a distance, and is the first to fall in love.

MIRANDA. I might call him
A thing divine, for nothing natural
I ever saw so noble. (1.2.491-493)

When they're closer together, Ferdinand instantly succumbs to Miranda's ethereal beauty and wants to stay with her forever.

FERDINAND. Most sure, the goddess
On whom these airs attend! Vouchsafe my
prayer
May know if you remain upon this island,
And that you will some good instruction give
How I my bear me here. (1.2.498-503)

Prospero arranged for Ariel to bring Ferdinand to Miranda, and Prospero is delighted with the result, which he believes will help him to recover his dukedom in Milan.

PROSPERO. ... At the first sight
They have changed eyes. (1.2.523-524

Ferdinand proposes marriage even faster than Juliet proposed to Romeo in the balcony scene. (Romeo and Juliet, 2.2.148-154)

FERDINAND. O, if a virgin,
And your affection not gone forth, I'll make you
The Queen of Naples. (1.2. 531-533)

That's all that Prospero wants to hear for now, and he decides to slow down the romance.

PROSPERO. [to Ferdinand] Soft, sir! One word more.
[Aside] They are both in either's powers; but this swift
business
I must uneasy make, lest too light winning
Make the prize light. (1.2.534-538)

Prospero can't resist controlling Miranda and Ferdinand's relationship the same way he controls everything and everyone else on the island, but their love for one another exists beyond Prospero's sorcery. Ferdinand and Miranda overcomes every test and condition that Prospero imposes on them.

Ferdinand and Miranda's quiet, loving relationship is a stark contrast to the noisy, contentious relationships between and among all of the other characters on the island. Their relationship represents calm in the midst of the tempest of intrigue and revenge swirling around them.

This is clearly exemplified in act 5. Prospero is trying to resolve the many complex and confusing issues of the play. Prospero leads Alonso into Prospero's home, where they discover Ferdinand and Miranda, quietly playing chess, oblivious to the chaos outside.

Ferdinand and Miranda are apparently having their first argument, which, compared to every other argument on the island, is respectful, loving, remarkably civil, and wholly lacking in merciless, vengeful intent.

[Here Prospero discovers Ferdinand and Miranda playing at chess]

MIRANDA. Sweet lord, you play me false.

FERDINAND. No, my dear'st love,
I would not for the world.

MIRANDA. Yes, for a score of kingdoms you should wrangle,
And I would call it fair play. (193-197)

Ferdinand and Miranda's love is a reminder to everyone else of their own temporarily lost humanity. Prospero renounces his sorcery, freedom is restored to servants and masters alike, order returns to the island, and happiness reigns.

The relationship between Miranda and Ferdinand in The Tempest is important because it provides a still point at the center of an (appropriately) tempestuous world. There's something less than human about the other characters in the play, of which Caliban is only the most extreme example. Miranda and Ferdinand, however, seem incredibly normal by comparison. Perhaps this is the main reason why so many critics have tended to see them as rather dull, uninspiring characters. But this is a tad unfair.

The main purpose of Miranda's relationship with Ferdinand is to allow her to discover herself as a human being, who and what she really is. Prior to Ferdinand's arrival she has never seen a single human being other than Prospero and the somewhat less-than-human Caliban. But in due course she develops a take on humanity that is at once both touchingly naive and strangely perceptive:

O wonder!

How many goodly creatures are there here!

How beauteous mankind is! O brave new world,

That has such people in’t!

And these are the people who banished her father! Of course, Miranda doesn't know this yet, but she still provides us with a perspective on humanity that her father, for obvious reasons, cannot. So Miranda comes to grow and blossom as an important person in her own right, one endowed with intelligence, charm and compassion.

At the same time, however, she cannot truly escape the prevalent norms of society, despite having grown up apart from that society. Her relationship with Ferdinand has immense political repercussions; their intended marriage is, in keeping with Elizabethan norms, to be a dynastic one. It's somewhat ironic that Miranda discovers her sense of humanity only then to be turned into a commodity to be bought and sold in a highly competitive marriage market.

But alas, Miranda must serve the needs of society just as her relationship with Ferdinand must serve the needs of the play, leading as it does towards a final reconciliation between Prospero and the world that turned him into an outcast.

The function of the relationship between Miranda and Ferdinand in this play seems to serve a number of different functions. On the one hand, Ferdinand's union with Miranda is something that is deliberately stagemanaged by Prospero, who, it is clear, ordered Ariel to separate Ferdinand from his father and his father's retainers so he can be lead by Ariel towards a separate part of the island, where he can meet Miranda and the two can fall in love. Note what Ariel tells Prospero about what he has done with the sailors in Act I scene 2:

The King's son have I landed by himself,

Whom I left cooling of the air with sighs

In an odd angle of the isle, and sitting,

His arms in this sad knot.

At every stage, Miranda and Ferdinand's relationship is carefully overseen by Prospero, who, with the precision of a director, manages their time together and their feelings towards each other. This is on the one hand part of Prospero's plan to return to his home country and take up his former position. Marrying his daughter to the king's son can only secure his return to power and also secure her future. However, at the same time, critics have pointed out the way in which Miranda is presented as nothing more than a meek, obedient daughter, who stands by whilst her father and future husband talk casually about Ferdinand taking her virginity. What is stressed through this relationship is Prospero's power, not only over spirits and creatures such as Caliban, but over those who are, in theory, nearest and dearest to him.