My husband does not trust me. He has no reason not to, in fact if anyone should not be trusted it would be him. But he always comes and checks up on me and freaks out if I forget my phone or don't answer his call. What should I do?
What should he do?

It sounds like he is projecting onto you. You said he is the one to not be trusted and usually when someone is doing bad things they will accuse the other person of wrongdoing in order to deflect any accusations before they are flung.

It sounds like you guys need to figure out what is going on with your marriage. Do you think your husband would be open to couples counseling?

Pick a quiet time in the day when the two are semi relaxed and then whack him over the head with a 2X4 (nail in the end optional) and tell him you want his complete attention.

Ask him what have you ever done to cause him to mistrust you! After you flatten that topic, then move on to why you have trouble trusting him.

Trust once broken is very difficult to repair.