As the eldest Stark child in Winterfell, Robb had spent much of years traveling with his father as part of diplomatic envoys. He had sat in on Ned's meetings with important men, attended feasts and watched as the Lord of Winterfell carried out acts of justice against criminals and oathbreakers. His younger brother Bran had often been bored to tears by all the politics, but Robb had always paid rapt attention and tried to learn from and emulate his father whenever he could. Ned Stark was the perfect example of an honourable Northern lord, and Robb had grown up with the knowledge that one day he would be expected to take up his father's mantle.
Their trip to Storm's End was, however, the first that they had embarked upon as equals: Ned had returned to his rightful place as Lord of Winterfell, and Robb had found himself delivered from the grave and King in the North once more. Of course, upon their reunion Robb had offered the Northern crown to his father - it was only right. Robb had not chosen to be king, but he had risen to the occasion under the support of his northmen, and he knew that to fail to offer the position to Ned would be too easily taken as impertinence. However, Ned's only desire had proven to be finding the rest of Robb's scattered siblings and protecting Winterfell, and he had refused the crown.
So it was that the duty of treating with Stannis Baratheon had fallen to Robb, who considered himself fortunate to be traveling in Ned's company. Although a king, Robb still found it a comfort. Together, he knew that they must ally Robb's forces with Stannis if they hoped to put the rightful king on the Iron Throne and separate the North.
Robb kept one hand on the hilt of his sword as they were led by Stannis' men, returning his father's look with a nod. With the power of Storm's End and Renly's men behind him, Robb knew that this alliance could prove very fruitful indeed. His face remained a mask of calm composure, but Robb's whole body felt shot through with taut nerves. Like his father, he saw the promise of battle and bloodshed in every contingent of armed men that they passed by on their way to meet with Stannis himself.