Learn Russian: Этот проект соответствует стандарту качества. - This project matches the quality standard.

The verb соответствовать (to match, to correspond to) requires the Dative case for the thing being matched. This is the Dative of Matching, where a subject lives up to or conforms to an external rule or standard.

Is there a trick to remembering why соответствовать triggers the Dative?

Look at its root: ответ (answer). Just like the verb отвечать (to answer) takes the Dative for the person receiving the answer, соответствовать literally means to co-answer or answer to. The project is figuratively answering to the standard.

Why is качества in the Genitive case instead of agreeing with the Dative стандарту?

The word качества (of quality) modifies стандарту. When a noun describes another noun, the second noun takes the Genitive case. It does not change cases to match the first noun because it acts like a possessive attribute, not an adjective.

Does соответствует have a perfective pair for when the project finally matches the standard?

No, it is an imperfective-only verb. It describes a continuous state (the project is currently in a state of matching the standard). Verbs that describe ongoing relationships or states of being rarely have perfective pairs because there is no single completed action to emphasize.