Rank
They wear Crimson helmets and under-armor with large semi-circular orange 'plates' sticking into the air. These 'plates' also have yellow and red alternating patterns, bordered by black. This yellow/red alternating pattern is also seen on the thrones of High Prophets. It is unknown if they are the highest rank or in another rank class entirely, but some things support that they are equal in rank with the Ultra Elite. Shine your light on their back or leg as the Master Chief, and you'll see that these Elites are pink. For the first: Both ranks can become Honor Guard Ultras, and for the second: An Honor Guard is less active than a Zealot, making many people to believe that they're one step lower than Zealots, and that's equal with Ultra Elites. This is speculation, but it is believable. Or it could be that to maintain their skills they spar with each other or possibly with training programs the Covenant have developed. Also since the changing of the guard is so heartbreaking to the elites it could be that the honor guards are second only to the arbiter among the Elites.
It seems that wherever a High Prophet is present, the Honor Guard are also. There could be as many as 300 Honor Guard Elites for each Prophet, as the Step of Silence seems designed to hold 300 Honor Guard but only one Prophet. They are commanded by the more skilled Honor Guard Ultras.
Combat
Up until the changing of the guard, seen before the level Sacred Icon in Halo 2, these Elites were the personal bodyguards of the Prophet Hierarchs. They were replaced when the Brutes took over, just before the Civil War of the Covenant. Honor Guard Elites' armor could take as much damage as that of an Elite Major. They fought usually with Energy Swords and occasionally have Plasma Rifles, double Plasma Rifles and Carbines. They also wield the ceremonial Honor Guard Pike that match their armor (only in cutscenes). More wiry and agile than the Brute honor guards, their speed and quick reflexes with the Energy Sword paired with their skill with double Plasma Rifles rapid fire made them formidable foes. The Elite Honor Guards are only seen in cutscenes and the levels Delta Halo, Regret, and Gravemind as enemies. It seems that once the Covenant Civil War began Guards took back their armor as some Elite Honor Guards can be seen fighting Brutes in the level Gravemind.
Trivia
A Minor Elite with Honor Guard armor can be seen on a page in the Halo 2 Official Strategy Guide