The question is illogical because there was no such thing as a viking in the days of the undivided Roman Empire or of the Western Roman Empire.
A viking is defined as a Scandinavian pirate or sea raider during the period of about 795 to 1100 AD at the widest.
It is always incorrect to capitalize viking and use it as an ethnic word instead of an occupational word.
Thus it is impossible for western Romans before 476 AD to ever encounter vikings since no Scandinavians ever went on viking raids to Roman territories until after the western Roman Empire fell.
But Roman citizens and subjects and Scandinavians did meet sometimes.
For example, Roman artifacts have been unearthed from Scandinavian Roman era sites.
Each artifact was either transported to Scandinavia in stages, passing from one trader to another, or else was transported to Scandinavia in one long trip.
In the latter case, either Scandinavians acquired Roman artifacts in Roman territory, thus meeting Roman citizens and subjects, or else Roman traders and/or diplomats transported them to Scandinavia, thus meeting Scandinavians.
And there were Saxon sea raiders who raided the "Saxon Shore" of Roman Britain and Gaul during the late empire.
In those days the Romans used the word "Saxon" to refer to not only Saxons, but other northern Germanic peoples who raided Roman lands by sea.
Thus it is possible that some of those "Saxons" were Angles, Jutes, and other Scandinavians.
If there were any Scandinavians among those "Saxons" making proto-viking type raids on Roman lands, they might have used the word "viking" to describe their occupation.
Of course modern historians would not approve of using the word "viking" to describe such raiders centuries before the age of vikings.
And as written in andejons' answer, the Roman battles with the Cimbrians may have been with migrants from Scandinavia.
There were a lot of Germanic mercenaries in the Roman army, and SOME of them MIGHT have been Scandinavians.
Radagaisus, a Gothic King, led a horde of barbarians in an invasion of Italy in 405-406 before being defeated by Flavius Stilicho.
The invaders included Alans, Sueves, and Vandals.
I have read that some of the barbarians came from far north, and thus it is POSSIBLE that SOME of them were born in Scandinavia.
And considering that there were contacts between Romans and Indians and Chinese, there could have been some unrecorded contacts of various types between Romans and Scandinavians.
So the answer is vikings no, Scandinavians yes.
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I presume you're not talking about the Byzantine half of the Roman Empire here.
Those ties are well known.
So, taking the subject line of your question, Romans of the western half of the Roman Empire meeting Vikings would be impossible because Rome fell before the label Viking was generally applied to Scandinavians.
Taking the text of your question, the answer regarding trade is yes, but mainly through intermediaries .
Regarding seriously scouting for invasion, I don't think so, but one cannot prove a negative.
history.stackexchange.com/users/12036/o.m.
Leaving aside the questions whether Scandinavians during the first centuries CE could be called "vikings", the answer is that they did encounter them.
The Cimbrians were a people who invaded Italy and fought the Romans about 100 BCE.
The Cimbrians are said to have come from the Cimbrian peninsula, identified with Jylland in Denmark.
As for Roman invasions of Scandinavia, there was really no way or point to it since they could and would not control continental Germania following the battle of Teutoburg forest.
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No they did not.
The romans, I suspect, never came up that far north.
They did, however deal with the similar goths.
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The Roman Empire, that is to say, the Western half of the Roman Empire, had fallen /collapsed around 476 AD/CE, approximately 325 years before the first Viking ships set sail from Scandinavia.
When the Vikings emerged on the world historical stage, Rome, as well as much of the Italian peninsula, were slumbering through "The Dark Ages".
So chronologically speaking, it would have been impossible for The Romans to have had any type of encounter with The Scandinavian Vikings.
Geographically speaking, as far as we know, the Romans never traveled towards Scandinavia; the most Northern city within The Roman Empire was Cologne in Northwest Germany/
The Rhineland-(or
if you prefer, York, in Northern England).
The last architectural Roman remnant in Northern Europe, is Hadrian's Wall, located in the North of England-(though you could also include the Antoinne Wall in Southern Scotland).
In short, the Romans, even during the final years of their Empire, would probably have not known of the existence of Scandinavia or its indigenous peoples and certainly would have not known of or encountered The Vikings.
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Did the Romans ever scout Scandinavia for possible conquest? Or was trade ever done between them?
Did the Romans ever encounter the Vikings?
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<roman-empire><vikings>
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The vikings were not around at the same time as the Romans. However, Romans and Scandinavians did meet each other.  It would have been impossible for the Romans to come into contact with the Vikings as they existed during very different periods of history. However, there is disagreement as to whether or not the Romans interacted with Scandinavians, though they may have done or at least traded through intermediaries.
It would have been impossible for the Romans to come into contact with the Vikings as they existed during very different periods of history. It is unclear whether Romans came into contact with Scandinavians as it would be geographically rather difficult and possibly without much point. It is possible that Romans came into contact or traded with Scandinavains through intermediaries.