At long last these procedures have been removed from the G450 Operating Manual but FlightSafety still uses them as a required maneuver so here are some techniques.
I adopted using HUD symbology on the PFD long ago and the reaction was, at first, stunned amazement on how well I could perform the maneuver. It was, many said, a result of my thousands of hours in the simulator and natural, steeley-eyed, military aviator expertise. But now it seems many others are adopting HUD symbology on the PFD and discovering it is simply a matter of taking advantage of technology.
What follows comes from the references shown below. Where I think it helpful, I've added my own comments in blue.
[G450 Aircraft Operating Manual (Historical) §06-03-00 Figure 1.
There are several methods: PFD traditional, HUD, and PFD with HUD symbology
Figure: Typical Climb to Altitude, from G450 Aircraft Operating Manual §2B-05-00, Figure 18.
You more than likely will not have the flight director, but no matter. The aircraft symbol will typically be about 2-1/2° nose high when starting the maneuver. (This will vary according to the altitude and speed chosen for the exercise.) Fly the airplane along a cardinal heading and roll smoothly to 45° of bank, adding back pressure and trim passing 30° of bank. Once the bank is established, crosscheck the altitude and speed, adjust as necessary. The G450 rolls more crisply than the G-III or G-IV and only 10° lead is needed for the roll out.
Figure: HUD at 45° Bank, from Eddie's Notes
The HUD can be used for steep turns, but it isn't easy. The horizon line on the HUD is a “relative” horizon, but there will be a gap where the flight path vector is. Keep the flight path vector on the relative horizon with a crosscheck of the altimeter. Keep the acceleration caret centered and your power is set correctly for the bank angle, make changes based on the speed error tape. Remember that pitch changes that look large on the HUD are actually smaller than they appear. You can prove this to yourself in the right seat by bringing up the HUD on a DU while the left seat pilot flies.
Figure: PFD at 45° Bank, from Eddie's Notes
The best method is to switch the primary flight display to HUD symbology. Unlike the HUD, the PFD has a gray line with a white dot where the HUD has a gap in the horizon line. You need only keep the flight path vector on that white dot to guarantee level flight. The acceleration caret on the left wing gives you instant speed cues.
Gulfstream G450 Aircraft Operating Manual, Revision 35, April 30, 2013.
Gulfstream G450 Aircraft Operating Manual (Historical), Revision 24, September 18, 2009.
Gulfstream G450 Airplane Flight Manual, Revision 35, April 18, 2013