I'm trying to draw another shape to go with this heart, and I want the line on which the anchor is selected to have exactly the same curvature as the corresponding length on the heart. Is this possible, or is the only way to eyeball it?
In a nutshell, you duplicate the exiting path, delete what you don't want, then add what you do want to the duplicate.
Use the Direct Selection Tool (the white arrow) and hold down the Option/Alt key to drag a copy of the path to a new area.
Now, use the Pen Tool and click on the path to place new anchors where you want to cut the path. Basically, make certain anchors are at the start and end of the section you want to keep.
Now, using the Direct Selection Tool again, click one of the anchors you don't want to keep and hit the delete key. Repeat this for each anchor you do not want to retain. You will be left with only the section of path you want to use.
At that point simply grab the Pen Tool again, click one of the exiting anchors and continue drawing. This will give you the section with matched the original section identically.
I guess that making a path copy of the heart, enlarging it and just working out your shape from that path might work.