Work on fixed installations (faste installationer) has to be done by an autoriseret elinstallatørvirksomhed (authorised electrical firm). Ask whether they hold the authorisation themselves or bring someone who does, and get that on the invoice.
Aarhus mixes apartments in the centre with houses in Højbjerg, Tilst and Viby J. The drive across Ringvejen, and access in older stairwells, is what usually separates two quotes. The same 5 businesses as the Danish page: Vietz El-installation A/S, Stautrup El ApS, Martin Juhl El Teknik ApS, Hessellund & Rokkedal El A/S, Rafn El ApS.