Quartz.net uses Common.Logging, so something like this in your App.config/Web.config:
<configSections>
<sectionGroup name="common">
<section name="logging" type="Common.Logging.ConfigurationSectionHandler, Common.Logging" />
</sectionGroup>
</configSections>
<common>
<logging>
<factoryAdapter type="Common.Logging.Simple.**youradapterhere**, Common.Logging">
<arg key="level" value="ERROR" />
</factoryAdapter>
</logging>
</common>
<arg key="level" value="ERROR" /> <!-- add this line here -->
