Historically, Utvær had a very robust fishing industry and in 1858, the greater Utvær area was split off from the municipality of Eivindvig to become its own municipality known as Utvær.
hɪstˈɔːɹɪkli, ˈʌtvɛɹ hæd ɐ vˈɛɹi ɹoʊbˈʌst fˈɪʃɪŋ ˈɪndʌstɹi ænd ɪn wˈʌn θˈaʊzənd ˈeɪthˈʌndɹɪd fˈɪfti ˈeɪt, ðə ɡɹˈeɪɾɚɹ ˈʌtvɛɹ ˈɛɹiə wʌz splˈɪt ˈɔf fɹʌmðə mjuːnˈɪsɪpˈælᵻɾi ʌv ˈiːvɪndvˌɪɡ tə bɪkˌʌm ɪts ˈoʊn mjuːnˈɪsɪpˈælᵻɾi nˈoʊn æz ˈʌtvɛɹ.