If you have a 150 DPI (dots per inch) JPG or TIFF this can be easily converted to EPS for the printer. If you only have 72 DPI which is the standard for web graphics then the best bet is to make a new logo at a higher resolution.
Let me know if you need help with the file conversion and I can do this quickly in Adobe. It would be good to know what dimensions you are planning to print the logo on the mat. Based on the JPG/TIFF I can give you an idea what the maximum supported dimension is without it looking stretched or distorted. Send me a PM if you would like help.
PS - Holy shit I just noticed you were promoted to Brown not too long ago. Don't know how I missed that. Congrats!