When problems arise, people care about two things:
1) how bad it is, i.e. what is the IMPACT on the project?
2) what you are doing about it, i.e. what is the SOLUTION?
So when communicating bad news, be crystal clear about what it means and what options you have identified to resolve the situation. Project sponsors typically don't have a lot of time and don't appreciate being thrown a problem with no solution in sight. By articulating clearly what the problem means for the project (and the sponsor) and presenting solutions, you give confidence to your sponsor that things can be resolved, you show them that you are proactive and can be trusted, and this is a very effective basis for getting them to actually help you (for example if you need them to make a decision or to exercise their influence to get things going).
In terms of conveying the message, I think that especially in situations where the impact is high, face-to-face communications work best. When you talk to your sponsor, also remember to validate with him/her how the bad news (and the way forward!) should be communicated to the wider project stakeholders' audience (in some cases the message may need to come from the sponsor for example).