We have a few hints and suggestions for what might have passed for meditation in classical Stoicism.
Most of these come down as words from the Koine (Greek), and a little from Latin.

Melete, (Μελέτη):  The Muse of Meditation.
Premeditatio: Premeditation (e.g.:  Premediatio Malorum).
Askesis, (ἄσκησις):  Training.
Pneuma, (πνεῦμα):  Breath, (often used by the Stoics as Spirit).
Psyche, (ψυχή):  Breath of Life, Soul, Spirit.

Epictetus advises us many times to maintain a tranquil mind, a mind impenetrable to outside causes.  Marcus engages in several visualization and mind-calming exercises.  We have the Delphic Injunction to “Know Thyself.”  In looking at the above list of vocabulary words, we see a lot of similarity in other School’s meditation vocabulary, specifically from the Indian subcontinent.

There has been some speculation that the “gymnosophistai” which Alexander came across in his travels were either Jains or early Buddhists.  We have ended up with a bottle-necking of Stoic sources, and there are references and terms to things which suggest some sort of meditation practice.

Musonius also discusses two types of trainings for the philosopher, those which train the body, and those which train the mind/soul.  He doesn’t enumerate nor elaborate on these, but the hints from Epictetus and Musonius suggest to me something akin to meditation.

Whether this is sitting meditation as most folks understand it, or more intellectual exercise is up for debate.  Lately, I’ve been learning Vipassana mediation as a support for my Stoic practice.  At the danger of sounding like an eclectic, I think that there is a high degree of possibility for this helping my practice.

This, and following the Rule of Musonius (a set of seven rules extracted from his Lectures and Sayings), I think I’ve found an interesting vehicle for practice.  I’ll be publishing the seven rules in the next few weeks, and, Fate permitting, the full e-book not too long thereafter.

I discussed this issue in an Ask A Stoic video, as well: