How to Recapture a Mouse (or other rodent)
Remy is definitely a cutie! :)
As an owner of many, many rodents over the years, I have also had my share of "escape artists". One trick I've learned is after an escape, you can place a small aquarium (5.5 gallon tanks are big enough) on the floor in the room where you think the rodent is (normally next to a wall, since rodents like run close to walls).
Place books and such next to the tank so that the rodent can climb into the tank. Put the lid next to the tank (you can even use the lid as a ramp to allow the rodent to get inside the tank). Place a bit of bedding from their cage along with some dry food and a shallow dish of water into the aquarium, but most importantly put a running wheel in the tank too! Several times I have heard the wheel being used, quietly walked over to the tank and quickly covered it with the lid - rodent rescued!
Often the food and water aren't even needed to get the animal into the tank (rodents love to run in wheels!), but in case you're not around when they've explored the tank, consumed food/water (plus new poop) is a good way to confirm that you've had a visitor.
If the animal is especially hard to catch (maybe you're not around often enough to catch them exercising), you can try using a tall empty wastebasket (tall enough to keep them from jumping out - and they can jump pretty high!), again with a bit of bedding, food & water inside. Cover the top of the wastebasket with sheet or two of paper laying loosely across the top. Often the rodent will smell the food or bedding, explore the wastebasket, and walk across the paper 'lid' - which will fall into the wastebasket along with the rodent. Make sure you check this trap at least twice a day to avoid abandoning your pet.
Both of these techniques have worked many times for me in the past, though the best story I heard was from a friend who had house mice visit the open tank simply to use the wheel (no food or water was in the tank). As I said, rodents love to run in wheels! :D