Sys.WebForms.PageRequestManagerServerErrorException: The conversion of a varchar data type to a datetime data type resulted in an out-of-range value.

As per the Error ,
it seems there are mainly 2 possibilites this error could arise.
1.) If you are doing any operation (INSERT/UPDATE) and using a SP/INLINE code please check the parameters passed in SP or INLINE CODE.

2.)The Operations you are carrying please check the table schema and datatype for the particular problem.

Hope this helps.
Is possible can you attach code so that it will be easy to rectify.
And one more thing do check the culture on your local machine and one where you are deploying the application

1. You are probably using incorrect datatypes. Why do you need to convert date to varchar or vice versa?
2. To me it seems a locale issue. In your settings, date format may be dd/mm/yy whilst on the server it may be mm/dd/yy. So, 13/01/11 will work on your computer but may not work on the deployed version.

This is why choice of correct datatypes is very important. Try to remove the conversion from your application to be safe.

Are u using calendar control with default attached textbox.
try to check with default date of your calendar to your database.