In Act 1, Scene 2 of The Tempest, Ariel sings a song that guides Ferdinand to Miranda. They fall for each other, each initially thinking the other is some spirit. Miranda is also quite lonely. "This / Is the third man that e'er I saw, the first / That e'er I sighed for" (I.ii.448-450). The "sighed for" indicates an affection or that she's fallen in love with Ferdinand. Having been on the island for 12 years, she is quite frustrated with her father for being so discourteous to Ferdinand since this may be her only opportunity to find love, let alone simply speak to another human being.
Ferdinand proposes that she become the Queen of Naples. He believes his father, the King of Naples, is dead and assumes he is now King. His offer to Miranda is marriage. When Prospero imprisons Ferdinand believing their relationship is moving too quickly to have any genuine meaning, Miranda is of course upset, having seen no ill will in Ferdinand's demeanor or words. Not to mention, she has fallen in love with him. However, at the end of the scene, she reassures Ferdinand by telling him that her father's actions here are unusual, hoping that there must be some ulterior reason.