Searching the attic
One of the features of our house that I like the least is that the only attic access is through a pull-down ladder in our master bedroom's closet. To open it, you have to remove all the clothes, pull out the pole, unscrew four supports, and take out the shelf. This closet runs the length of our bedroom, so this is a significant undertaking.
So the first step was to go up in the attic and take a look. I found a bunch of scat, a moldy chewed citrus rind, and insulation popped up. We figured it was probably one or more squirrels, since we have quite a few around and we've heard them running across of roof quite frequently, but knew it could also be a rat or something else. Ann was guessing something the size of a opposum or water buffalo ("Can't you hear how it moves with a lot of weight?"). Learned quite a bit about squirrel infestations online here.
I kept trying to run up the ladder (very, very quietly, as Madeleine was usually sleeping) when we heard it making noise, but it remained elusive. One time I tried peeking under the insulation and pushing it down at different spots which resulted in some scurrying, but I still couldn't see it. As I looked more carefully, I found more droppings spread around the attic.

I found a spot under our roof line where the trim was coming off and a fair amount of light was making its way into the attic. A couple contractors who looked into it for us found some better candidates, and I was able to confirm one as the likely entry point, since there was scat right on the inside.
I also found that the opening for our oven range vent exhaust had a very loose opening giving easy access for a rodent to the attic (something neither contractor noticed).
But unless we wanted to end up smelling some dead rodent for months, we would need to catch the intruder before we patched things up.
Catching the critter
One of our neighbors a block away has been trapping squirrels in her yard, so we were able to borrow a live trap from her. I was able to put it in the attic, baited with peanut butter, in the early afternoon. We didn't hear any activity until about 11:30pm, when we heard scratching and what sounded like activity near the trap (but no sound of the trap shutting). After a couple hours of minimal sleep, we heard the trap shut at about 1:30am. Ann wanted me to wait until morning to deal with it, but it was making enough noise that it became clear pretty quickly that we weren't going to get any more sleep that night unless we dealt with it. Madeleine was blissfully sleeping through it all, though.

(I was forbidden from putting a picture of the actual "gross" critter on our home page, so you'll have to click through the censored image.)
Liberating said critter
So I decided it would be best to release our captive right away, even though it was quite early in the morning. I put on my thick leather gloves, placed newspaper under the cage, and carried it down the narrow pull-down ladder and right past Madeleine blissfully sleeping (where Ann was ready to protect her). The newspaper was a good idea, as the rat was relieving itself in its angst along the way.
The cage went in the car trunk with more newspaper underneath it, and I drove out of Alameda over the Bay Farm Bridge. Some sites I had read talked about squirrels finding their way back a few miles after being dropped off. The rat would have to swim the estuary or navigate the bridge, though.
I picked a park right on the estuary and adjacent to a golf course and the Oakland Airport, as it's out of the way and far from homes. Since it was after hours, the gate was closed, so I pulled up right outside the gate, put on my hazard lights, and walked back to the trunk. As I was walking back, I saw some headlights and thought, "Hmm, there aren't too many people out at this time. Hope
I don't end up explaining this to a police officer."
Sure enough, a sheriff's car pulls up behind me, shining a spotlight on me in my leather gloves getting ready to pull something out of my trunk. I probably looked like a psychopathic killer getting ready to dump a dead body into the estuary. The conversation went something like this:
Sheriff: Can I help you with anything?
Me: Well, I just caught this roof rat in my attic, and I was going to release it here. Is that okay?
Sheriff: You caught a rat, huh? How did you catch it?
Me: In this live cage. My neighbor loaned it to me.
Sheriff: (Shines flashlight into my trunk.) Yeah, that's a rat. Um, okay. There's just not many people out here at this time.
Me: Yeah, well, I have a newborn daughter and it was making noise right above our bedroom. We have enough problems keeping her asleep.
Sheriff: You have a newborn daughter?
Me: Well, she's four months old.
Sheriff: Sure, four months old. They don't sleep very well. Okay, carry on.
He took off, and I carried the cage into the parking lot and tried to figure out how to open the thing to let it out without it jumping on me (it was pretty freaked). I finally did so and it ran out, switched back toward me, and ran toward the estuary. Then I think I heard a little splash. I'm hoping it could either swim or it found some shallow water.
I know there are mixed recommendations on releasing rodents back outside, some saying they have a hard time surviving when they're transplanted. But we figure we'd rather let nature take its course.
We've had the trap back up in the attic, but haven't heard any activity since then. We're having the entry points sealed this week. Maybe someday Madeleine will thank me.