Concept:
Pessaries are solid dosage forms intended to be inserted into the vagina.
Step 1: Understanding pessaries.
Pessaries are used for local action in the vaginal cavity. They may contain antiseptics, antifungal agents, hormones, or other drugs.
Step 2: Route of administration.
Since pessaries are inserted into the vagina, their route of administration is the vaginal route.
Step 3: Why other options are wrong.
Rectal route is used for suppositories.
Nasal route is used for nasal drops, sprays, and insufflations.
Pulmonary route is used for inhalation preparations.
Step 4: Final answer.
Hence, pessaries are administered by the vaginal route.
\[
\boxed{\text{Vaginal}}
\]