It is virtually impossible to estimate the cost of antique furniture restoration. So much depends on so many factors that most restorers would need to either see the object or at least see a digital photo of the object before they can assess it.
If you have an antique chair which needs restoring, you have to look at three major factors. The first is the seat and whether it is upholstered, woven, solid wood or other type. If the seat is woven this is subject to high restoration fees depending on the expert undertaking the project. Specialist material may be required and costs such as this are hard to guess.
Tables and Drawers
Table tops can be defined by their grain, as to which wood has been used and the best way to restore it. In the case of table tops and chests of drawers the top could be make from a veneer which will need replicating to meet the standard of the age of the antique. Also, in some cases there could be deep scoring and scratching, which requires French polishing. That is highly specialist and not come cheap.
Bookcases and Other Furniture
Again, wood type is a factor here and also the extent of any damage caused to the piece. A specialist may end up charging more than the item is financially worth. It all resides in the fact that the piece is of such high sentimental value that it is worthy of the costs.