Depending on how your plan was provisioned, there are different behaviors for what happens when the database size limit is exceeded.
Plans added through www.RavenHQ.com
The free plan has a fixed size limit and an exception will be thrown if you attempt to write data to the database once the size limit has been reached.
On all paid plans, when your database goes over its limit, we'll charge an additional storage fee (metered daily and measured by the byte) until you have the chance to upgrade your plan. You can continue paying overage fees indefinitely, but we encourage you to upgrade to a plan that is designed for your data storage needs so that you experience the best performance at the most sensible price.
Plans added through AppHarbor or Azure Marketplace
All plans provisioned through either AppHarbor or the Azure Marketplace have fixed size limits, as those platform providers don't support the necessary billing features that would allow us to offer per-GB billing for over usage scenarios. Once your database size has reached the limit of the plan, exceptions will be thrown when attempting to write to the database.
If you are interested in per-GB billing, we recommend provisioning a plan directly on www.ravenhq.com.