I also do well in interviews.
Some big tips from being on both sides - be prepared - already have the answers for typical interview questions. Know as much as possible about the company and the job. When answering questions, give specific examples to support your answers. For example if you say you are organized then state an example in your past experience that proves you are organized. Anyone can say they have a certain trait, but if you support it with actual real life examples you provide proof. Tell the interviewer you are interested in the position. This is a good conclusion type of thing. I really like what you have said about your company and the position. I would like you to know I am very interested. Have good pertaintent questions prepared - I even bring a written list of them with me. And follow up with a quick letter - email is fine now and is quicker just giving a good short thank you for their time and to re-enforce your interest and qualities.