What I would do is write a thank you letter. Thank them for their time and consideration. Within this short email or letter, give a quick highlight of your qualifications and your interest. It is important to keep the line of communication open. This will help to keep you uppermost in their mind should they have a job that fits your qualifications. I would then say maybe write in a couple of weeks to check in - maybe send them an article you read they might find of interest, etc. That way you keep that communication and are providing something as well.