One possible way is to use Labeled
g1 = Plot[Sin[x], {x, -2 Pi, 2 Pi}, Frame -> True, FrameLabel -> {{"f(x)", None}, {"x", "sin(x)"}}];
g2 = Plot[Cos[x], {x, -2 Pi, 2 Pi}, Frame -> True, FrameLabel -> {{"f(x)", None}, {"x", "cos(x)"}}];
g = Grid[{{g1, g2}}];
Framed@Labeled[g, Style["My amazing plots", Red, 16], Alignment -> {Bottom, Center}]
You can also use just Grid, like this
lbl = Style["My amazing plots", Red, 16];
Framed@Grid[{{g1, g2}, {lbl, SpanFromLeft}}, Alignment -> Center]
