Drupal's calendar module is a great tool for building calendars quickly with views. However, the default theme is still using tables, blech! After some searching, I came across a sandbox module to fix this, https://drupal.org/node/1675894#comment-7903527. Like some of the user's in that thread, I did not want to add another module to my site. So, I set off to theme the calendar in a responsive way. Surprisingly, this was much easier than I anticipated. You only need to override two theme files and add roughly 88 lines of css.
We had a Drupal 7 site setup with a default calendar instance that was displaying content of type 'event'. Due to the limited number of events this site would promote, it was decided to change the navigation from the standard 'Next/Previous' to use drop down menus where the user could choose the month/year they wanted to view.