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Broil it for roughly the same amount of time.
For fish, the cook time is generally 7-10 minutes per inch (thickness) of fish. Like half pint says, broiling is probably a great way to go, but the timing will likely depend more on the thickness of your fish than what the recipe directs.
Think of a broiler as an upside-down grill. Just be careful not to overheat / burn the glaze. You can regulate the amount of heat by adjusting the distance to the heating element.
Cooking by time = bad idea. Purchase a digital thermometer if you don't have one. You need 140F to kill possible parasites.
You can modify the straight grilling / broiling technique by allowing the glaze to get bubbly under the broiler and then switching to oven heat until the fish reaches a proper temperature. And you can do the reverse, oven heat until almost done, finish under the broiler which is probably what I would do for maximum control.
As ChefOno says 'oven heat, then broil'.
Also, if this is a regular problem, there are stove-top pans you can buy that simulate grilling and work really well with fish.