Ujjain gives the verse's ninth peetha two addresses, and the busier of the two is not the one that carries the name.
Ujjain is the only city in India that holds a jyotirlinga and one of these eighteen at once, and it is the one place in the set where a reader can be sent to the wrong temple with complete confidence on both sides. The stotra names the ninth peetha at Ujjain and calls the goddess Mahakali. Two temples answer to that. Gadhkalika, in the old quarter near the Bhartrihari caves, is a Kali shrine and is what the accounts that read the verse carefully point at. Harsiddhi, on the eastern bank of the Rudra Sagar tank a short walk from Mahakaleshwar, is the temple with the crowds, the two forty-foot lamp columns lit at Navaratri, the Vikramaditya legend and a state tourism page calling it a Shakti Peetha — and it appears in the fifty-one and fifty-two lists under its own limb. So the question is not which shrine is genuine. Both are old and both are seats of the goddess. The question is which one this particular hymn's ninth line means, and the honest answer is that the line says Ujjain and does not say which side of the city.
Claims, and where they come from
Ujjain is one of the eighteen Shakti Peethas of the recited enumeration, named ninth, and the goddess there is called Mahakali. — Aṣṭādaśa Śakti Pīṭha Stotra (traditionally attributed to Śaṅkarācārya) — Third verse, opening half — ujjayinyāṁ mahākālī, pīṭhikāyāṁ puruhūtikā — pairing Ujjain with Pithapuram, which is the next member and also in this corpus. The attribution of the hymn to Shankaracharya is traditional; this corpus writes attributed to rather than composed by. The verse names a city and a goddess and stops, which is why the shrine is disputed below
No limb of Sati is assigned to this site by the enumeration that names it. — The structure of the stotra itself — The eighteen carry no limb assignments. An upper lip is given for Gadhkalika and an elbow for Harsiddhi, both from the separate fifty-one-peetha convention. That the two Ujjain temples carry different limbs in that convention is worth noticing on its own: the larger lists treat them as two distinct seats, not as one seat under two names, which is a fact about those lists rather than an answer about this one
Three of the eighteen stand in a city that also holds a jyotirlinga — Srisailam, Ujjain and Varanasi — and not four. — This corpus's own reading of the two enumerations it carries — Set out on the shakti_peetha set page. The fourth site usually added to that count is Vaidyanath, which belongs to the fifty-one and the fifty-two and not to this eighteen. Ujjain's jyotirlinga, Mahakaleshwar, is a separate site file in this corpus: it shares the city but no compound, so it is a second site rather than a second membership
The Harsiddhi temple's present structure is of the Maratha period, and its lamp columns are lit during Navaratri. — Modern record and the practice of the shrine — Carried as received rather than as established. Accounts consistently describe a Maratha-period rebuilding, commonly associated with Ahilyabai Holkar, over a much older foundation, and the two lamp columns are a living Navaratri practice anyone can observe. The attribution of the original foundation to Vikramaditya is legend and is recorded here as legend; no inscription or scholarly treatment supporting it was reached from this session
Counted among
The Shakti Peethas — Sati's body fell across the subcontinent — and the tradition has never agreed on how many pieces, or on how many shrines.
Questions to explore
Ujjain has two temples that both answer to the ninth line of this hymn, and each carries a different limb in the larger lists. Does that mean one of them is wrong, or that the city has always had two seats?
Ujjain holds a jyotirlinga and a peetha at once. Is that a coincidence of an old capital being crowded with shrines, or did the two circuits pull towards each other?
The verse names cities, not temples. Was it composed for people who already knew which shrine was meant, and what does it cost us that we no longer do?