For Project Server 2013 we issued a public update in March, which is a required patch going forward for loading all  future Cumulative Updates, such as the April CU.  However, there was an issue with the Project Server part of the patch which would lead to an error when running the SharePoint Configuration Wizard.  The error in the upgrade logs would be something like the following, with an EventID of ajxnf:

WARNING           Project Web Instance 'SharePoint - 80:PWA' can only be upgraded once its database 'ProjectWebApp' has been upgraded

ERROR                Cannot upgrade [ProjectSite Name=f959de76-c4e9-4fa7-91a5-d9d9e287714b]. 38c20f9c-fdcc-b07a-f785-09836d46c179

and the error at the end of the configuration wizard, or in the PSCDiagnostics logs would be something like:

ERR                  Task upgrade has failed with a PostSetupConfigurationTaskException

An exception of type Microsoft.SharePoint.PostSetupConfiguration.PostSetupConfigurationTaskException was thrown.  Additional exception information: Failed to upgrade SharePoint Products.

This would be repeated for each PWA site in your farm.  The fix for this issue is in the April Cumulative Update for Project Server 2013. The roll-up package including the SharePoint fixes for April has been delayed (at the time of writing expected w/c 4/22) – but if you are in this state currently and want to complete the configuration wizard then loading the individual Project Server 2013 April CU is certainly an option – see http://support.microsoft.com/kb/2760261.

If you have yet to install the March Public Update then I would suggest delaying until the full roll-up patch including SharePoint Server 2013 is released and then you can load the March PU, then the April CU and finally run the configuration wizard, which will avoid the failure noted above.

As always, please open a support incident if you need any assistance with any of the above steps.