C# Signature:

[DllImport("advapi32.dll", SetLastError=true, CharSet=CharSet.Auto)]
[return: MarshalAs(UnmanagedType.Bool)]
static extern bool LookupPrivilegeValue(string lpSystemName, string lpName,
    out LUID lpLuid);

VB Signature:

Declare Function LookupPrivilegeValue Lib "advapi32.dll" (lpSystemName As String, _
   lpName As String, ByRef lpLuid As LUID) As Boolean

User-Defined Types:

LUID

Use the following symbolic names:

public const string SE_ASSIGNPRIMARYTOKEN_NAME = "SeAssignPrimaryTokenPrivilege";
public const string SE_AUDIT_NAME = "SeAuditPrivilege";
public const string SE_BACKUP_NAME = "SeBackupPrivilege";
public const string SE_CHANGE_NOTIFY_NAME = "SeChangeNotifyPrivilege";
public const string SE_CREATE_GLOBAL_NAME = "SeCreateGlobalPrivilege";
public const string SE_CREATE_PAGEFILE_NAME = "SeCreatePagefilePrivilege";
public const string SE_CREATE_PERMANENT_NAME = "SeCreatePermanentPrivilege";
public const string SE_CREATE_SYMBOLIC_LINK_NAME = "SeCreateSymbolicLinkPrivilege";
public const string SE_CREATE_TOKEN_NAME = "SeCreateTokenPrivilege";
public const string SE_DEBUG_NAME = "SeDebugPrivilege";
public const string SE_ENABLE_DELEGATION_NAME = "SeEnableDelegationPrivilege";
public const string SE_IMPERSONATE_NAME = "SeImpersonatePrivilege";
public const string SE_INC_BASE_PRIORITY_NAME = "SeIncreaseBasePriorityPrivilege";
public const string SE_INCREASE_QUOTA_NAME = "SeIncreaseQuotaPrivilege";
public const string SE_INC_WORKING_SET_NAME = "SeIncreaseWorkingSetPrivilege";
public const string SE_LOAD_DRIVER_NAME = "SeLoadDriverPrivilege";
public const string SE_LOCK_MEMORY_NAME = "SeLockMemoryPrivilege";
public const string SE_MACHINE_ACCOUNT_NAME = "SeMachineAccountPrivilege";
public const string SE_MANAGE_VOLUME_NAME = "SeManageVolumePrivilege";
public const string SE_PROF_SINGLE_PROCESS_NAME = "SeProfileSingleProcessPrivilege";
public const string SE_RELABEL_NAME = "SeRelabelPrivilege";
public const string SE_REMOTE_SHUTDOWN_NAME = "SeRemoteShutdownPrivilege";
public const string SE_RESTORE_NAME = "SeRestorePrivilege";
public const string SE_SECURITY_NAME = "SeSecurityPrivilege";
public const string SE_SHUTDOWN_NAME = "SeShutdownPrivilege";
public const string SE_SYNC_AGENT_NAME = "SeSyncAgentPrivilege";
public const string SE_SYSTEM_ENVIRONMENT_NAME = "SeSystemEnvironmentPrivilege";
public const string SE_SYSTEM_PROFILE_NAME = "SeSystemProfilePrivilege";
public const string SE_SYSTEMTIME_NAME = "SeSystemtimePrivilege";
public const string SE_TAKE_OWNERSHIP_NAME = "SeTakeOwnershipPrivilege";
public const string SE_TCB_NAME = "SeTcbPrivilege";
public const string SE_TIME_ZONE_NAME = "SeTimeZonePrivilege";
public const string SE_TRUSTED_CREDMAN_ACCESS_NAME = "SeTrustedCredManAccessPrivilege";
public const string SE_UNDOCK_NAME = "SeUndockPrivilege";
public const string SE_UNSOLICITED_INPUT_NAME = "SeUnsolicitedInputPrivilege";

Notes:

Int64 (or long in C#) could be used instead of LUID.

Tips & Tricks:

Please add some!

Sample Code:

public const int ANYSIZE_ARRAY = 1;
public const int SE_PRIVILEGE_ENABLED = 0x00000002;

[StructLayout(LayoutKind.Sequential)]
public struct LocalIdAndAttribute
{
    public long Luid;
    public int Attributes;
};

[StructLayout(LayoutKind.Sequential)]
public struct TokenPrivileges
{
    public int PrivilegeCount;
    [MarshalAs(UnmanagedType.ByValArray, SizeConst = ANYSIZE_ARRAY)]
    public LocalIdAndAttribute[] Privileges;
};

TokenPrivileges tkp = new TokenPrivileges
     {
    PrivilegeCount = 1,
    Privileges = new LocalIdAndAttribute[1] {
        new LocalIdAndAttribute { Attributes = SE_PRIVILEGE_ENABLED }
    }
    };
if (!LookupPrivilegeValue(null, SE_SHUTDOWN_NAME, out tkp.Privileges[0].Luid))
{
    int error = GetLastError();
    WriteLine("LookupPrivilege failed - Error = {0}", error);
}

Alternative Managed API:

Do you know one? Please contribute it!