Ancient authors mention the presence of ships from Alexandria in Puteoli a couple of times. Suetonius describes the enthusiasm of the Egyptian sailors when they happened to see Augustus:

Forte Puteolanum sinum praetervehenti vectores nautaeque de navi Alexandrina, quae tantum quod appulerat, candidati coronatique et tura libantes fausta omina et eximias laudes congesserant: per illum se vivere, per illum navigare, libertate atque fortunis per illum frui.

As Augustus sailed by the gulf of Puteoli, it happened that from an Alexandrian ship which had just arrived there, the passengers and crew, clad in white, crowned with garlands, and burning incense, lavished upon him good wishes and the highest praise, saying that it was through him that they lived, through him that they sailed the seas, and through him that they enjoyed their liberty and their fortunes.

Suetonius, Divus Augustus 98.2. Translation J.C. Rolfe.

The transport of grain in bulk to Puteoli is referred to by the geographer Strabo, and in a letter the philosopher Seneca gave a lively description of the arrival of the Alexandrian grain fleet:

Anyone might judge, if he were at either Alexandria or Dicaearchia, and saw the merchant vessels both at their arrival and at their departure, how much heavier or lighter they sailed thither or therefrom.

Strabo, Geography 17,1,7. Translation H.L. Jones.

Subito nobis hodie Alexandrinae naves apparuerunt, quae praemitti solent et nuntiare secuturae classis adventum: tabellarias vocant. Gratus illarum Campaniae aspectus est: omnis in pilis Puteolorum turba consistit et ex ipso genere velorum Alexandrinas quamvis in magna turba navium intellegit; solis enim licet siparum intendere, quod in alto omnes habent naves. Nulla enim res aeque adiuvat cursum quam summa pars veli; illinc maxime navis urgetur. Itaque quotiens ventus increbruit maiorque est quam expedit, antemna summittitur: minus habet virium flatus ex humili. Cum intravere Capreas et promunturium ex quo alta procelloso speculatur vertice Pallas, ceterae velo iubentur esse contentae: siparum Alexandrinarum insigne est. In hoc omnium discursu properantium ad litus magnam ex pigritia mea sensi voluptatem, quod epistulas meorum accepturus non properavi scire quis illic esset rerum mearum status, quid adferrent: olim iam nec perit quicquam mihi nec adquiritur.

Suddenly there came into our view today the Alexandrian ships, I mean those which are usually sent ahead to announce the coming of the fleet; they are called mail-boats. The Campanians are glad to see them; all the rabble of Puteoli stand on the docks, and can recognize the Alexandrian boats, no matter how great the crowd of vessels, by the very trim of their sails. For they alone may keep spread their topsails, which all ships use when out at sea. Because nothing sends a ship along so well as its upper canvas; that is where most of the speed is obtained. So when the breeze has stiffened and becomes stronger than is comfortable, they set their yards lower; for the wind has less force near the surface of the water. Accordingly, when they have made Capreae and the headland whence tall Pallas watches on the stormy peak, all other vessels are bidden to be content with the mainsail, and the topsail stands out conspicuously on the Alexandrian mail-boats. While everybody was bustling about and hurrying to the waterfront, I felt great pleasure in my laziness, because, although I was soon to receive letters from my friends, I was in no hurry to know how my affairs were progressing abroad, or what news the letters were bringing; for some time now I have had no losses, nor gains either.

Seneca, Epistulae IX,77,1-3. Translation R.M. Gummere.

The translation of Seneca's words contains a little error. The crowd is standing in pilis: not on the docks, but on the great mole in the harbour. Incidentally we learn that private mail arrived from Alexandria, perhaps also picked up elsewhere, and that special ships were used for that purpose, the naves tabellariae.

Very large ships were also required for the transport of obelisks, in which Puteoli played an essential role:

Alii duo sunt Alexandreae ad portum in Caesaris templo, quos excidit Mesphres rex, quadragenum binum cubitorum. Super omnia accessit difficultas mari Romam devehendi, spectatis admodum navibus. Divus Augustus eam, quae priorem advexerat, miraculi gratia Puteolis perpetuis navalibus dicaverat; incendio consumpta ea est. Divus Claudius aliquot per annos adservatam, qua C. Caesar inportaverat, omnibus quae umquam in mari visa sunt mirabiliorem, in ipsa turribus Puteolis e pulvere exaedificatis, perductam Ostiam portus gratia mersit. Alia ex hoc cura navium, quae Tiberi subvehant, quo experimento patuit non minus aquarum huic amni esse quam Nilo.

There are two other obelisks, which were in Caesar's Temple at Alexandria, near the harbour there, forty-two cubits in height, and originally hewn by order of King Mesphres. But the most difficult enterprise of all, was the carriage of these obelisks by sea to Rome, in vessels which excited the greatest admiration. Indeed, the late Emperor Augustus consecrated the one which brought over the first obelisk, as a lasting memorial of this marvellous undertaking, in the docks at Puteoli; but it was destroyed by fire. As to the one in which, by order of the Emperor Caius, the other obelisk had been transported to Rome, after having been preserved for some years and looked upon as the most wonderful construction ever beheld upon the seas, it was brought to Ostia, by order of the late Emperor Claudius; and towers of Puteolan earth being first erected upon it, it was sunk for the construction of the harbour which he was making there. And then, besides, there was the necessity of constructing other vessels to carry these obelisks up the Tiber; by which it became practically ascertained, that the depth of water in that river is not less than that of the river Nilus.

Pliny the Elder, Naturalis Historia 36.14.70. Translation J. Bostock - H.T. Riley.

The first obelisk, transported in the ship that was on display in Puteoli and destroyed by fire, was placed in 10 BC on the spina of the Circus Maximus. Today it is in the centre of Piazza del Popolo. The obelisk that was transported by Caligula is now on Saint Peter's square.

Piazza del Popolo with Augustus' obelisk. Photo: Wikimedia, WolfgangM.