Many smartwatches offer users the chance to customise the design.
One watch-face website said it acted swiftly to remove copyrighted designs.
Smartwatches are available from a range of firms including Samsung, Sony and LG. Next year Apple will launch a version.
According to TorrentFreak, Richemont - the company behind brands such as Cartier IWC and Panerai - has lodged notices against watch-face sites citing breaches of its trademark rights. In some cases, TorrentFreak reports, it is giving sites 24 hours to remove infringing content.
"We prefer to never comment on trademark protection issues," Richemont told the BBC.
Swatch-owned Omega, also highlighted by TorrentFreak as requesting take-downs, did not respond to requests for comment either.Defending brands
Sites such as Facerepo offer users the chance to download a traditional face on to their smartwatches.
It describes itself as "a repository of watch-faces for Android Wear devices" but goes on to say that "all faces hosted on the site are the property of the original content creator".
It told TorrentFreak that it acts quickly to remove watch-faces that are infringing copyright.
"Although some of the replica faces we've received take-downs for are very cool-looking and represent significant artistic talent on the part of the designer, we believe that owners of copyrights or trademarks have the right to defend their brand," it told the news site.
Last week, Apple released its WatchKit developer tools, allowing developers to begin creating apps for the Apple Watch.
Currently those tools do not support the creation of custom watch-face designs.