Analogue-styled watches.

You can enable Settings > Developer options > Stay awake to keep your device awake while it is charging.
Depending on your device you may have the option to set the screen timeout to "never" under Settings > Display > Sleep.

Note: If you don't see Developer options in Settings, it may be made available by going to to Settings > About > Build number. Developer options should appear after tapping the build number several times.