I have a 98 Honda Civic DX that my windshield wipers and odometer/speedometer decided to quit working at the same time. We checked the fuses and they have not blown. They thought is might be
The windshield wiper motor, but the odometer is not working either. I was told I am getting power.
I have not had any issues to date with either of them. What should I check?

Hi,
I am not trying to be sarcastic, but I think maybe you should check with a local, reputable, garage repair person.
Sounds like you have a short in your electrical wiring, and they, sometimes, are very, very hard to find. A good repair person will have the instruments needed to find it, hopefully, fast.
It's too much of a coincidence that both quit working at the same time, and probably are connected in some way. I do wish you the best of luck.

Although some things ground through the mounting bolts, others use a ground wire. Pull the plug off the wiper motor. Does it have at least 3 wires one of which is black? Check the black from the harness to see if it is grounded. If not, follow it and see if it is loose or broken somewhere. If another wire joins it, that could be the ground from the odometer. I am sure you were already aware you could take it to the dealer.

Crocivic often give good answers on Honda stuff. He may even be able to check the ground in his manual.

If it was a short, the fuse would have blown. I am sure you were already aware you could take it to the dealer.

Hi,
I am, also, sure you were aware you could take it to the dealer! However, that was not my advice, as suggested by another answer here. Maybe he misunderstood my definition of "garage".
My advice was to take it to a good, reputable garage! A dealer charges an arm and a leg for most anything. A good repair person, in a garage, can find the problem for you, normally cheaper, than a dealer.
By "garage", I mean an independent, or private, garage... not a Dealer Repair Shop. Sorry I didn't make that more clear, but thought the person asking the question would know the difference.
The reason I am suggesting a good garage, instead of trying to "do it yourself", is because issues like this can take a long time, especially if the wiring is in a harness. If you have the time, then go for it. If not, have it looked at by a reputable garage repair person.

Those 2 units are on different fuses, so obviously two fuses had to blow if the problem was with the fuse.

However, check number 15 fuse again (vehicle speed sensor is connected to this fuse - should be 7.5 amp) and number 26 fuse (wiper fuse - should be 20 amp).

Have you had anything done to your car before it stopped working? Try to see if the electrical connector is still connected to the vehicle speed sensor. The sensor is located on the transmission, with it's connector connected from above.

Do the turn signals work fine? Do you have the rear wiper? Does it function?

Did you check the fuses in the fuse box under the hood?