Ok, no need for the example, calling WebGrid1.ClientAction.Refresh() solved the problem. 

Thank you very much!

In fact it is a 3rd party object that does the database commands. 

Here is the VB.NET code: 

Private Sub WebGrid1_AddRow(ByVal sender As Object, ByVal e As ISNet.WebUI.WebGrid.RowEventArgs) Handles WebGrid1.AddRow
    	Dim cells As New ISNet.WebUI.WebGrid.WebGridCellCollection
    	cells = e.Row.Cells
    	If cells.Item(0).Text <> "" Then		
    		   UpdateSchedule(cells)               				   
    	End If
End Sub

Private Sub UpdateSchedule(ByVal cells As ISNet.WebUI.WebGrid.WebGridCellCollection)
      
	Dim rsSchedule As TxAppFramework.Core.Metabase = New TxAppFramework.Core.Metabase(1000000110, TxSession)            
	rsSchedule.Data.Open()
	rsSchedule.Data.AddNew()
	rsSchedule.Data.Value("SERVICEMEMORANDUM_ID") = Context.Request("RecordID") 
	rsSchedule.Data.Value("TIME") = cells.Item(0).Text
	rsSchedule.Data.Value("V_PAP_CAR_TYPE_ID") = cells.Item(1).Value
	rsSchedule.Data.Value("ADDRESS") = UCase(cells.Item(2).Text)
	rsSchedule.Data.Value("DRIVER") = UCase(cells.Item(3).Text)
	rsSchedule.Data.Value("V_PAP_SCHED_TYPE_ID") = cells.Item(4).Value
	rsSchedule.Data.Value("NO_CARS") = cells.Item(5).Text
	rsSchedule.Data.Value("NOTES") = cells.Item(6).Text)	
	rsSchedule.Data.Update()
	
	'This is where the ID is read and set in the Grid cell
	cells.Item(8).Value = CStr(rsSchedule.Data.ID())  
	cells.Item(8).Text = CStr(rsSchedule.Data.ID())
	rsSchedule.Data.Close()
	rsSchedule = Nothing
End Sub

So the new identity is returned  by the "rsSchedule" object,

and is set as the value and text of the cell corresponding to the column that has the key field (index #8). Is there somewhere else it should be set?

Finally got it working. When hitting "Copy SmartWebResource to Project Folder" in Deployment Manager, 

I realized it copied the DLLs to the root of the website, not in the Bin folder. 

After copying thoses DLLs from the root to the Bin folder, the message went away.