You can use PostMan for such task. ServiceAPI is just another Commerce website so with proper EPiServerLog.config you would get the right error in the log 

Ok. Can I get like a map over calls I can perform? I am using the tool SOAPUI to try out the REST API. I have tried calling: www.mysite.com/episerverapi, but get a fail in return.

https://world.episerver.com/documentation/developer-guides/Episerver-Service-API/ probably is what you need? 

Quan: What do you mean that service api is just another episerver web site? Surley it is not set up as an extra site in IIS?

When you install ServiceApi.Commerce to a IIS website, it turns into an Episerver Commerce site.

Actually setting up ServiceAPi as a separate site is more common than you might think. It's a good practice because it separates things, and you can hide your ServiceAPI endpoint inside safe firewall (it is not supposed to expose to public) 

The logging for episerver service api does not work for me. I think the configuration in episerverlogs.log looks fine, but nothing is written to the log file. Here is what my appender looks like: 

  <appender name="PimIntegrationFileLogAppender" type="log4net.Appender.RollingFileAppender" >
    <!-- Consider moving the log files to a location outside the web application -->
    <file value="..\Logs\Pim\PimIntegration.log" />
    <encoding value="utf-8" />
    <staticLogFileName value="true"/>
    <datePattern value=".yyyyMMdd.'log'" />
    <rollingStyle value="Date" />
    <threshold value="Debug" />
    <lockingModel type="log4net.Appender.FileAppender+MinimalLock" />
    <appendToFile value="true" />
    <layout type="log4net.Layout.PatternLayout">
      <conversionPattern value="%date [%thread] %level %logger: %message%n" />
    </layout>
  </appender>

I now realized that wrong name was used in the referer when specifying this logger.