Vertical align with :after

gistfile1.txt

.outer {
    width: 200px;
    height: 500px;
    
    text-align: center;
    background-color: #ffc;
}

.outer:after {
    display: inline-block;
    height: 100%;

    vertical-align: middle;
    content: "";
}

.inner {
    display: inline-block;
    width: 100px;

    vertical-align: middle;
    background-color: #fcc;
}