A Dictionary of Greek and Roman Antiquities, John Murray, London, 1875 covers custom duties in the Roman Empire at some length:
PORTO′RIUM was one branch of the regular revenues of the Roman state, consisting of the duties paid on imported and exported goods: sometimes, however, the name portorium is also applied to the duties raised upon goods for being carried through a country or over bridges (Plin. H. N. XII.31; Sueton. Vitell. 14). A portorium, or duty upon imported goods, appears to have been paid at a very early period, for it is said that Valerius Publicola exempted the plebes from the portoria at the time when the republic was threatened with an invasion by Porsenna (Liv. II.9; cf. Dionys. V.22).
As regards the articles subject to an import duty, it may be stated in general terms, that all commodities, including slaves, which were imported by merchants for the purpose of selling them again, were subject to the portorium; whereas things which a person brought with him for his own use, were exempted from it. A long list of such taxable articles is given in the Digest (Dig. 39 tit. 4 s.16; cf. Cic. c. Verr. II.72, 74).
In the time of Cicero the portorium in the ports of Sicily was one-twentieth (vicesima) of the value of taxable articles (Cic. c. Verr. II.75); and as this was the customary rate in Greece (Böckh, Publ. Econ. p325, 2d edit.), it is probable that this was the average sum raised in all the other provinces. In the times of the emperors the ordinary rate of the portorium appears to have been the fortieth part (quadragesima) of the value of imported goods (Suet. Vesp. 1; Quintil. Declam. 359; Symmach. Epist. V.62, 65).
The portorium was, like all other vectigalia, farmed out by the censors to the publicani, who collected it through the portitores.
The Serbian government's customs administration department has this little titbit:
The Romans also used to levy such duties as state and provincial or city taxes. As early back as the Roman times customs duties made up a significant part of public revenues for the state treasury. At certain communication points in the provinces there were customs stations (stationes) where the duties were charged for the goods passing such points. The amount of duties was 2.5% (quadrogesimo) of the value of imported goods. The collection of customs duties was also farmed out, at the beginning granted even to farmers from the ranks of domiciled population, and later on, from mid-2nd century on, duties were collected by officials that in our territory were called publicum portarii Illyrici et ripae Thraciae. In the Middle Ages, in addition to import and export duties, the so-called transit duties were also levied.
To summarise, Roman publicani via portitores levied customs duties during import as well as transit which, at different points in time, were anywhere between 2.5% to 12.5% of the value of the goods. All goods were taxed including slaves. Some exemptions were made with respect to personal luxuries.
I expect that World History of the Customs and Tariffs by Hironori Asakura will have oodles of information on this subject.