To confirm:
* Affirm: "I affirm that I will be there."
* Assert: "I assert my right to privacy."
* Declare: "He declared his love for her."
* Guarantee: "I guarantee you'll enjoy the show."
* Promise: "I promise to call you later."
To express certainty:
* Know: "I know that I'm right."
* Believe: "I believe in you."
* Be sure: "I am sure about this decision."
* Be certain: "I am certain of her innocence."
* Be convinced: "I am convinced that it's true."
To express strong intention:
* Intend: "I intend to finish this project by Friday."
* Plan: "We plan to go on vacation next month."
* Decide: "I have decided to move to a new city."
* Determine: "She determined to overcome her fears."
The best verb to use will depend on the specific context and what you are trying to convey.