Wikipedia has a long list of people with the name ヴェロニカ. Of course, this is all subject to the assumption that "Veronica" is pronounced near the English way. I think it is, but I don't know if the "v" is pronounced differently (like the German-English difference). Also, in Swedish, is the accent on the "ro"? This is tremendously important to giving you the correct answer.
SHADOW: ベロニッカ sounds like "ve-ro-ni'-kka" when you want the accent on the "ro" instead: "ve-ro'-ni-ka."
Here's the Wikipedia disambiguation page mentioning various saints, actresses, journalists, etc., named Veronica:
ヴェロニカ - Wikipedia
When it doubt about katakanization, go to Wikipedia, grab someone in your native language with the name you want, and look up their Japanese Wikipedia page.
Edit: @Vigge,
You sound like a reasonable person. Please don't go do something so idiotic as get something tattooed on you when you don't speak the language enough to know that it means what you think it means. Go to
Hanzi Smatter 一知半解 before getting any tattoo in a language you don't speak.
But I don't think you're saying you want to get a tattoo of your name in kana. So please continue thinking that way.