When looking for synonyms for the phrase "with assurance," there are a few options to choose from. Some examples include with conviction, with certainty, confident, sure, and certain. Each of these phrases emphasizes a feeling of initial confidence or trust in the situation at hand. For example, if you say "with assurance" that you will be able to complete a task, you are expressing your confidence that you understand the requirements and have the ability to accomplish what is needed. You might use the phrase "with conviction" to convey that you have a strong belief in a particular idea or concept that you are discussing. Likewise, the phrase "with certainty" emphasizes that you have no doubt about your ability or the outcome of a situation.