A strategy to use would be the following (assuming your APEX is sending one (1) email message; adapt code for more than one accordingly. The key is the method Messaging.reserveSingleEmailCapacity(someInteger) that you invoke before you send.

Messaging.SingleEmailMessage email = new Messaging.SingleEmailMessage(); try { Messaging.reserveSingleEmailCapacity(1); // SFDC throws exception if no headroom email.setToAddresses(...); ... Messaging.sendEmail(email); } catch (HandledException e) { // do something interesting like set up a retry mechanism for the next day // by persisting the message to send in some object and then having a daily // scheduled job resend the message at 0000h } 

There is a related post on this topic by @DougB

UPDATE

Prior to Winter 14, the reserveMassEmailCapacity existed but would throw an unhandled exception, this changed as per the Winter 14 Release Notes page 304

Updated Errors for Email Messaging Methods Errors have changed for the Apex Messaging methods reserveMassEmailCapacity and reserveSingleEmailCapacity, which are used when sending a mass or single email, respectively. If the transaction would cause the organization to exceed its daily email limit, using either of these methods results in a Handled Exception error. (Previously it resulted in a Limit Exception error.) The error that appears is: System.HandledException: The daily limit for the org would be exceeded by this request.

A strategy to use would be the following (assuming your APEX is sending one (1) email message; adapt code for more than one accordingly. The key is the method Messaging.reserveSingleEmailCapacity(someInteger) that you invoke before you send.

Messaging.SingleEmailMessage email = new Messaging.SingleEmailMessage(); try { Messaging.reserveSingleEmailCapacity(1); // SFDC throws exception if no headroom email.setToAddresses(...); ... Messaging.sendEmail(email); } catch (HandledException e) { // do something interesting like set up a retry mechanism for the next day // by persisting the message to send in some object and then having a daily // scheduled job resend the message at 0000h } 

There is a related post on this topic by @DougB

UPDATE

Prior to Winter 14, the reserveMassEmailCapacity existed but would throw an unhandled exception, this changed as per the Winter 14 Release Notes page 304

Updated Errors for Email Messaging Methods Errors have changed for the Apex Messaging methods reserveMassEmailCapacity and reserveSingleEmailCapacity, which are used when sending a mass or single email, respectively. If the transaction would cause the organization to exceed its daily email limit, using either of these methods results in a Handled Exception error. (Previously it resulted in a Limit Exception error.) The error that appears is: System.HandledException: The daily limit for the org would be exceeded by this request.

A strategy to use would be the following (assuming your APEX is sending one (1) email message; adapt code for more than one accordingly. The key is the method Messaging.reserveSingleEmailCapacity(someInteger) that you invoke before you send.

Messaging.SingleEmailMessage email = new Messaging.SingleEmailMessage(); try { Messaging.reserveSingleEmailCapacity(1); // SFDC throws exception if no headroom email.setToAddresses(...); ... Messaging.sendEmail(email); } catch (Exception e) { // do something interesting like set up a retry mechanism for the next day // by persisting the message to send in some object and then having a daily // scheduled job resend the message at 0000h } 

There is a related post on this topic by @DougB

A strategy to use would be the following (assuming your APEX is sending one (1) email message; adapt code for more than one accordingly. The key is the method Messaging.reserveSingleEmailCapacity(someInteger) that you invoke before you send.

Messaging.SingleEmailMessage email = new Messaging.SingleEmailMessage(); try { Messaging.reserveSingleEmailCapacity(1); // SFDC throws exception if no headroom email.setToAddresses(...); ... Messaging.sendEmail(email); } catch (HandledException e) { // do something interesting like set up a retry mechanism for the next day // by persisting the message to send in some object and then having a daily // scheduled job resend the message at 0000h } 

There is a related post on this topic by @DougB

UPDATE

Prior to Winter 14, the reserveMassEmailCapacity existed but would throw an unhandled exception, this changed as per the Winter 14 Release Notes page 304

Updated Errors for Email Messaging Methods Errors have changed for the Apex Messaging methods reserveMassEmailCapacity and reserveSingleEmailCapacity, which are used when sending a mass or single email, respectively. If the transaction would cause the organization to exceed its daily email limit, using either of these methods results in a Handled Exception error. (Previously it resulted in a Limit Exception error.) The error that appears is: System.HandledException: The daily limit for the org would be exceeded by this request.