There is a Serial Number Search feature that will display all Projects, Service Plans, Tasks, Purchase Order Receives (Item Receipts), and Service Orders that contain the Product.
One way to access this is on the Reports tab in the Project Explorer:
This will open following interface:
You can add as many serial numbers as you wish to the search:
When ready, click the Run button and your results will display:
The primary entity listed will be the Project where the Serial Number was found and if you expand the Project, all other entities found will be listed:
There is an Open Project button on the ribbon to open the Project, and you can click any of the other entities to open them to view/edit.
There are many fields that display in the grid due to how many different entities display, use the Auto-Fit All Columns button if desired:
This data can be exported to Excel or PDF format. The "Export transaction detail" determines whether just the list of Projects export or if all of the entities export as well.
You can also select any number of Products in the Project Editor, and from the Reports tab click Find Usages->Serial Numbers. This is also available via the right-click menu.