If the tab (page) name is unique across the portal, the following should work:
Dim tCtlr As New DotNetNuke.Entities.Tabs.TabController
Dim tInfo As DotNetNuke.Entities.Tabs.TabInfo = tCtlr.GetTabByName(tabName, PortalId)
Dim tID As Integer = -1
If Not tInfo Is Nothing Then
tID = tInfo.TabID
End If
If the tab name is not unique - that is, it is used on multiple child pages, the method GetTabByName can take a third parameter - that of the ParentTabID.