How much past due is the timing belt? I think newer Honda’s are spec’d for a replacement at around 100K miles, or 7-8 years. If rust is a limiting factor and you aren’t way past the recommended change-out, you best course may be just to cross your fingers and hope for the best. Honda wouldn’t say 100K miles if 50% of the belts broke at 101K miles. Most of the timing belts will last a good deal past 100K miles I expect.
There are websites such as this one that you can check: https://repairpal.com/estimator I saw one (not this one) that will send out a repair person to you and the price there was better than repairpal. I would suggest that you also get a new tensioner and water pump as the labor is the more costly item and it’s almost the same amount of labor to do all three.
Timing belt replacement cost. Replacing a timing belt for preventive reasons typically costs $500 to $900 . However, replacing a broken timing belt may cost up to $2,000 or more if it caused damage to the valves, pistons or water pump.
How could a broken timing belt damage a water pump?
Since the water pump and valves often run on the same belt (the timing belt), I can conceive that, rarely, a timing belt tensioner pulley may come apart and the parts could damage the water pump. I suppose broken pieces of the timing belt might also do that.
I’ve only every heard of the water pump going out and taking the timing belt with it, not the timing belt taking out the water pump.