Physicians like Dr. James Carmichael, who practised medicine in Virginia in the 1830s, often made concoctions and dispensed drugs without the benefit of a pharmacy. A mortar and pestle was an early mashing tool used for apothecary applications and herbs. Dr. Carmichael's wooden mortar and pestle is on display at the University of Virginia. Examples like this one can help you to date a mortar and pestle.
Look for a date. Many mortars have a date on the side, and the dates are generally accurate for the style, product and provenance or history. Mortars from the 1700s and into the 1800s were often dated.
Check the shape. Early mortars made of stone and marble were bowl shapes; later, the common shape became more like a cup. Deep mortars with handles came along later. Even the shape of the handle may help date the mortar and pestle. Look at the shape of the pestle, as well.
Check the product composition. Very primitive pieces may indicate an early date, or a tribal origin. Romans and Greeks used stone and marble mortars. Bronze and brass were common in the 1700s, and porcelain mortars appeared about 1780, according to the Herb Companion website. Cast iron mortars appeared about the time of the Civil War. More recent mortars may be glass, since the use of metals decreased at the turn of the 20th century as concern developed over the metal getting into the medication.
Consider the weight and wear. Old bronze and brass mortars are often very heavy while newer pieces are much more lightweight. The old pieces may have scratches from use and wear on the inside as well as on the bottom. New pieces available today, some made of green or white marble, may be identifiable by lack of wear.
Look at mortar and pestle photographs to compare your mortar and pestle with examples that give you ideas for style and shape, composition and weight. The pestle is often made from the same product as the mortar. The University of the Sciences in Philadelphia has museum mortar and pestle pictures available for study. Look at new and old sets for sale to develop a knowledge base for dating a mortar and pestle.