"Your certificate is with me."
Translation:Certificatul tău este la mine.
We don't use "cu mine" with objects. We use "la mine" with objects, with the meaning "in my possession".
We use both "cu mine" and "la mine" with persons and animals, with different meanings:
Maria este cu mine. = Maria is with me. --- where I am, no matter the place
Maria este la mine. = Maria is at my place. --- in my house