I understand that archeological finds such as clothing or jewelry can only be circumstantial, but how about grave stones, inscriptions or something like that?
Off the top of my head, there's three main strands of evidence:
Viking-Age females buried in Scandinavia wearing jewelry from Western Europe. The problem is that most women wearing Insular or Carolingian metalwork were probably actually wearing ornaments that had been picked up in plunder or maybe in trade. Three's a good number of brooches (dress pins) made from bible locks and relic boxes and that sort of thing. These sure look like plunder to me—not the kind of thing an Anglo-Saxon captive might wear with her on her journey to Norway.
Women found in double burials. When we find one person buried with a lot of grave goods alongside a woman who has nothing, it's possible that the woman was a captive or slave sacrificed at the funeral. We're improving our abilities to trace migration histories based on skeletal remains, and we're pretty good at identifying people who migrated (whether by choice or by force) during their lifetime, but we're still limited in our abilities to say where exactly they came from. There's a lot of possible cases, but to the best of my knowledge, we don't have any conclusive examples of a Western European female buried as a slave-sacrifice alongside a Viking-Age Scandinavian.
Textual accounts. These accounts are pretty vague—embarrassed, even—about captives being taken from Western Europe. The best account I know of comes from the biography of Saint Rimbert, who was a German bishop doing missionary during the mid-800s. His biographer recorded that when Rimbert got to the slave market in Hedeby (= Schleswig) in southern Denmark, a woman called out to him in Latin. She successfully advertised herself as a Christian well-versed in psalmody, and Rimbert bought aka 'liberated' her. (Other sources suggest that she would have joined his retinue, rather than returning to her home abbey.) The problem is that The Life of Saint Rimbert is a pretty sketchy biography. There's no early copies of it, and the copies that we do have contain a reference to Greenland—which wasn't discovered until over a hundred years after Rimbert's death. So it's really hard to tell just how much fact is buried in this rather exceptional account.
There's two other strands of evidence which I think are on a bit firmer ground, despite being somewhat tangential to the question at hand.
Irish female DNA in Iceland. DNA evidence can be very tricky, but it looks like most modern Icelanders descend from Norwegian males and Irish females. That's very suggestive, although we need to do more in depth analysis of DNA from the Viking Age itself. For example, it's possible that people of Irish ancestry might have been more genetically resistant to the Black Death, which would highly bias modern day population DNA. Moreover, it's likely that Scandinavian men moved to Ireland in the early 800s, intermarried with local women, and then their descendants moved to Iceland in the late 800s. So the Icelandic population may descend from female Irish slaves, but these slaves probably lived out their lives in new Scandinavian settlements like Dublin, rather than being taken back home to Norway or to a new home in Iceland. Nevertheless, the saga character of Melkorka is at least one example of a woman taken as a slave from Ireland to Iceland, albeit via a stop in the marketplaces of the Kattegat area.
Arabic reports of Norse slave traders. Most famously, Ibn Fadlan recorded in 922 that he witnessed a funeral among the Norse traders in modern-day Russia where they sacrificed a slave girl. This conforms to a larger body of Arabic geography literature from the period referencing slaves purchased from Norse traders. Archaeologically, we know that people adhering to Norse culture in Russia were closely connected with Sweden and other Scandinavian Norse speakers. From texts, we know that there were slave markets in the big trading towns like Birka and Hedeby. And we also know that viking raiders were at least occasionally taking people from Western Europe. If we connect the dots and ask ourselves where captives from the West and slaves in Scandinavia markets were going, some were probably being sold out into the Scandinavian hinterlands, but Scandinavia itself was not inhabited by major slave-consuming societies during the Viking Age. Instead, it looks to me like these markets, being fed from viking raids, were servicing the Norse merchants who traded with the Arabic world. We've got things like silver coins that made it all the way from their minting sites in Afghanistan to viking winter camps in England, and I think it's every bit as likely that at least some people were trafficked over long distances in the opposite direction.
So the long and short of it is that images of vikings abducting women are only rarely historically attested, and often under dubious circumstances. Nevertheless, a large body of tangential evidence converges to suggest that women were indeed abducted as part of the regular activity of viking raids (and early medieval warfare in general), and that at least some of these women got swept up into long-distance human trafficking. Nasty stuff, but unfortunately it's the sordid kind of history that erases itself from the historical record—slaves had very little chance to write their autobiographies or preserve their stories to posterity; the people who couldn't protect them were too embarrassed to talk about losing their women to viking raiders; and the people who bought them weren't going to humanize their slaves by writing biographies about them. That's a challenge historians today are only beginning to attempt to do.
Wow, thank you! That is incredibly interesting and I really appreciate you all taking the time to answer to thorougly. Especially, of course, textandtrowel!