The first step was to look at a lot of period mortars at 18th and early 19th century fortifications, which are rather thick on the ground in my neck of the woods. Today I probably would look at Google Images.
Next I took a number of spare gun tubes, specifically those from the old Airfix French Artillery. They are so thick and short as to be essentially useless as any known type of artillery as they stand. However, they are thick enough to stand in for a wide-mouthed mortar. I cut the tube to an appropriate length, knowing that the breech would not be seen.
Next I built the wooden block the mortar sits in out of suitably sized pieces of balsa wood. I gouged out the hollow in the top where the mortar tube would rest. I painted them appropriately and mounted them on a base painted to look like a freshly-laid platform of planks.
Because this was for gaming I didn't bother modelling the four hand-holds that protrude from either side. It would not be difficult to do, however. Four very small finishing nails or short pins could be readily inserted into the soft balsa wood sides of the base.