Start entering the blue outline as a new area. Let it completely cover the part of the boundary that you are interested in. Before saving the new area, right-click somewhere in the window to invoke the context menu and select Clip (accept the defaults). This will reduce the area and make it neatly follow the boundary you want to have as a line. Save the area now.
Convert the new area to a line (Ctrl-click the area to select it, go to the Transform pane, Convert - Convert to = line, Transform selection only, maybe Preview, then Transform).
Start editing the line (Alt-click it). Select all coordinates that are not on the boundary (Ctrl-click or Ctrl-drag), then delete them (eg, in the Info pane, see the Coordinates tab).
Also, check out this help topic: Start > User Manual > Editing > Clip