You can select a curved label on the map and drag it to a new location. It contours itself to the curve of the line segment at the new location. If the new location is too jagged for a curved label, then the label is rotated to the closest segment at the new location.
To drag a curved label to a new location, on the MAP tab, in the Selection group, click Select from the list. Select the label name on the map and drag it to a new location along the line segment. The line highlights while you drag it, to help you identify the line. The label's final location adjusts according to the position properties (such as position around the anchor point) set for the layer's labels. You can only drag one curved label at a time. If you have selected more than one, then you cannot drag anything.
You cannot drag curved labels away from their line. When a curved label is abbreviated and dragged to a new location, its original label expression is not restored.