An SQL export file of your current CMS database can be very large, especially if it includes cache tables. If zipping the file (you will be amazed of the compression rate for SQL files) does not decrease the size to a manageable one (e.g. under 30 MB which is the maximum size allowed by GMail now), the simplest way to send the file is, for example, by using one of these free (or at least with a free trial) online services:
In all of them, you upload the file using the web form they provide and they send an email to the person who needs to receive the file with a download link valid for a few days. You also have the possibility to use DropBox which is an option for intermediate size files.
Obviously, a complementary solution would be to reduce the size of the export file by making sure to only include the important tables in the export process and/or to empty the cache tables before starting the export.
Posted in: Migration process Sending large (SQL export) files