We just went through the same thing in January!
Our "PC" cat, baby of 21 and 1/2 years, almost a child to us, was put to rest (and it still brings tears to my eyes to write this) on January 15th.
I do KNOW what it feels like and she was our first child all those years I was desperately trying to start a family. Our son still thinks of her as a sister!
As we pack for our first trip since she's gone I find it hard not to pick up the phone and ask our neighbor to feed her as we usually do!
I'm usually the last person out of the house every morning and I used to say goodbye to her; now I say a quiet "Sleep with the angels, PC" as I walk out the door. It makes me feel better!
It may help to remember that you gave Muffin a good life!