This is your code, I just edited it to make it faster and easier to understand. I am not saying that it even works.
With ActiveSheet.Shapes
.AddTextbox(msoTextOrientationHorizontal, _
chartAreaLeft, _
plotAreaTop + chartAreaHeight + AfstandChart + 2 * AfstandKategorier, _
ForklaringBredde, 1.35 * ForklaringHøjde).Name = "spgOverskriftT" & "," & p
With .Range(Array("spgOverskriftT" & "," & p))
With .ShapeRange(1).TextFrame2.TextRange
.Characters.Text = "Tilpas"
.Font.Size = 11
.Font.Name = "Lucida Bright"
End With 'ShapeRange(1).TextFrame2.TextRange
With .ShapeRange
.Line.Visible = msoFalse
.TextFrame2.VerticalAnchor = msoAnchorMiddle
.Fill.Visible = msoFalse
.ZOrder msoBringToFront
End With 'ShapeRange
End With 'Range(Array("spgOverskriftT" & "," & p))
End With 'ActiveSheet.Shapes
If it works, this is how I would change it to get the values you're looking for. And I am not saying this will work, either
Dim Lft As Double
Dim Wdth As Double
Dim Tp As Double
Dim Hght As Double
With ActiveSheet.Shapes
.AddTextbox(msoTextOrientationHorizontal, _
chartAreaLeft, _
plotAreaTop + chartAreaHeight + AfstandChart + 2 * AfstandKategorier, _
ForklaringBredde, 1.35 * ForklaringHøjde).Name = "spgOverskriftT" & "," & p
With .Range(Array("spgOverskriftT" & "," & p))
With .ShapeRange(1)
With .TextFrame2
Lft = .Left
Wdth = .Width
Tp = .Top
Hgth = .Height
With .TextRange
.Characters.Text = "Tilpas"
.Font.Size = 11
.Font.Name = "Lucida Bright"
End With 'TextRange
End With 'TextFrame2.
'The rest is with ShapeRange
.Line.Visible = msoFalse
.TextFrame2.VerticalAnchor = msoAnchorMiddle
.Fill.Visible = msoFalse
.ZOrder msoBringToFront
End With 'ShapeRange
End With 'Range(Array("spgOverskriftT" & "," & p))
End With 'ActiveSheet.Shapes
Now you have the TextFrame's Lft, Wdth, Tp, and Hght to use as you want.