Heat a gas grill to high or prepare a hot charcoal fire.
Combine 1 Tbs. of the mayonnaise and the honey in a small bowl. Season the tuna steaks with 1/2 tsp. salt and 1/4 tsp. pepper and coat both sides with the mayonnaise mixture. When the grates are very hot, grill the tuna until dark marks form on both sides, 1 to 2 minutes per side for medium rare. (If you prefer medium tuna, grill over medium-high heat for about 3 minutes per side.) Transfer to a cutting board and let rest for 5 minutes. Slice into 1/4-inch-thick strips.
Cut the potatoes in half and toss them in a mixing bowl with the remaining 2 Tbs. mayonnaise, the mustard, and 1/2 tsp. salt. Turn the grill to medium high or let the fire die down some. Grill the potatoes without disturbing except to flip, until brown grill marks form on both sides, 1 to 2 minutes per side.
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