There are several available diagnostic tools (error tracing, 11g Diagnosibility, OCM, Process Memory Guides, RDA, OSW, diagnostic scripts) that collectively can prove powerful for identifying the cause of the ORA-4030. 

Error Tracing

The ORA-4030 error usually occurs on the client workstation and for this reason, a trace file and alert log entry may not have been generated on the server side.  It may be necessary to add additional tracing events to get initial diagnostics on the problem.

To setup tracing to trap the ORA-4030, on the server use the following in SQLPlus:

alter system set events '4030 trace name heapdump level 536870917;name errorstack level 3';

Once the error reoccurs with the event set, you can turn off  tracing using the following command in SQLPlus:

alter system set events '4030 trace name context off; name context off';

NOTE:   See more diagnostics information to collect in Note 399497.1

 11g Diagnosibility

Starting with Oracle Database 11g Release 1, the Diagnosability infrastructure was introduced which places traces and core files into a location controlled by the DIAGNOSTIC_DEST initialization parameter when an incident, such as an ORA-4030 occurs.  For earlier versions, the trace file will be written to either USER_DUMP_DEST (if the error was caught in a user process) or BACKGROUND_DUMP_DEST (if the error was caught in a background process like PMON or SMON). The trace file may contain vital information about what led to the error condition.  

Note 443529.1 11g Quick Steps to Package and Send Critical Error Diagnostic Information
to Support[Video] 

Oracle Configuration Manager (OCM)

Oracle Configuration Manager (OCM) works with My Oracle Support to enable proactive support capability that helps you organize, collect and manage your Oracle configurations.

Oracle Configuration Manager Quick Start Guide
Note 548815.1: My Oracle Support Configuration Management FAQ

Note 250434.1: BULLETIN: Learn More About My Oracle Support Configuration Manager 

General Process Memory Guides

An ORA-4030 indicates a limit has been reached with respect to the Oracle process private memory allocation.    Each Operating System will handle memory allocations with Oracle slightly differently.

Solaris     Note 163763.1
Linux       Note 341782.1
IBM AIX   Notes 166491.1 and 123754.1
HP           Note 166490.1
Windows Note 225349.1, Note 373602.1, Note 231159.1, Note 269495.1, Note 762031.1
Generic    Note 169706.1