Finite elements with CFL condition - How to obtain correct order of convergence

I have discretized a PDE with continuous finite element method in spatial variable and with implicit Euler or Crank-Nicolson in temporal variable. In both cases, I have error estimates in $L_2$ norm in form $mathcal{O}(Delta,t^j + h^2),$ where $j=1$ for backward Euler and $j=2$ for Crank-Nicolson. In both cases I have a CFL contition of form $Delta,t = mathcal{O}(h^2).$ Therefore, when I run the code I always take $Delta,t = mathcal{O}(h^2).$ However, for this choice in backward Euler I have
begin{equation}
mathcal{O}(Delta,t + h^2) = mathcal{O}(h^2)=mathcal{O}(Delta,t).
end{equation}
Now, in Crank-Nicolson, for the same choice of $Delta,t$ I have
begin{equation}
mathcal{O}(Delta,t^2 + h^2) = mathcal{O}(h^2)=mathcal{O}(Delta,t).
end{equation}

My question : How can I conclude to second order accuracy in time for Crank-Nicolson when $Delta,t = mathcal{O}(h^2)$?