Edit in JSFiddle

jQuery(function($) {
    $('.with-height-limit').each(function(index, node) {
        var $outer = $(this);
        
        // wrap all children
        $outer.wrapInner('<div />');
        var $inner = $outer.children();
        
        // get heights of them
        var outerHeight = $outer.height();
        var innerHeight = $inner.height();
        
        // show ellipsis if inner block is higher than outer
        if (innerHeight > outerHeight) {
            $('<span />', {
                "class": 'ellipsis',
                text: '…'
            })
                .appendTo($outer);
        }
    });
});

<div class="text-overflow with-height-limit">
    <p>This is a long long long long long long long long long long text</p>
</div>
<div class="text-overflow with-height-limit">
    <p>This is a short text.</p>
</div>
<div class="text-overflow with-height-limit">
    <p>This is an another long long long long long long long long long long text</p>
</div>

.text-overflow {
    border: solid 1px #ccc;
    box-shadow: 1px 1px 4px rgba(0,0,0,.1) inset;
    line-height: 1.5em;
    margin: 1em;
    overflow: hidden;
    padding: 4px;
    position: relative;
    width: 200px;
}
.text-overflow .ellipsis {
    background-color: #fff;
    bottom: 0;
    position: absolute;
    right: 4px;
}
.with-height-limit {
    height: 3em;
}

h1 {
    font-weight: bold;
}
h1::after {
    content: ":"
}