The problem is with the location and size of the colorbar. By changing the Position of the colobar to the left i.e., reduce the left value of the position: [left bottom width height] you can see the complete colorbar but on the top of subplots 2 & 4.
For this particular problem I would suggest you to make a subplot grid of 2x3 instead of 2x2 so that you can make use of the space of 3 & 6 subplots and change the Position property of the colorbar accordingly. The following code will help you
figure
subplot(2,3,1)
[C,h]=contour(f_mat,sig_mat,real(L_lossy_mat).'*1e9,'LineWidth',2);
h.LevelList = [-1 -0.5 -0.2 -0.05 0.0 0.03 0.04 0.05 0.06];
clabel(C,h,'LabelSpacing',100,'FontSize',14,'FontWeight','bold','FontSmoothing','on','Interpreter','Latex')
ylabel('$\sigma^{(\textbf{I})}$ (S/m)','Interpreter','Latex')
xlabel('$f$ (MHz)','Interpreter','Latex')
title('$R=\infty$','Interpreter','Latex','Color',[125/255 30/255 125/255])
ax=gca;
ax.YDir = 'reverse';
ax.YScale = 'log';
ax.YMinorGrid = 'off';
ax.TickLabelInterpreter = 'latex';
xticks([37 46 55])
yticks([0.01 0.1 1 10])
yticklabels({'0.01','0.1','1','10'})
subplot(2,3,2)
[C,h]=contour(f_cst,sig_cst,real(L_11_cst).'*1e9,'LineWidth',2);
h.LevelList = [-1 -0.5 -0.2 -0.05 0.0 0.03 0.04 0.05 0.06];
clabel(C,h,'LabelSpacing',100,'FontSize',14,'FontWeight','bold','FontSmoothing','on','Interpreter','Latex')
ylabel('$\sigma^{(\textbf{I})}$ (S/m)','Interpreter','Latex')
xlabel('$f$ (MHz)','Interpreter','Latex')
title('$R=1.1r_0$','Interpreter','Latex','Color',[125/255 30/255 125/255])
ax=gca;
ax.YDir = 'reverse';
ax.YScale = 'log';
ax.YMinorGrid = 'off';
ax.TickLabelInterpreter = 'latex';
xticks([37 46 55])
yticks([0.01 0.1 1 10])
yticklabels({'0.01','0.1','1','10'})
subplot(2,3,4)
[C,h]=contour(f_cst,sig_cst,real(L_20_cst).'*1e9,'LineWidth',2);
h.LevelList = [-1 -0.5 -0.2 -0.05 0.0 0.03 0.04 0.05 0.06];
clabel(C,h,'LabelSpacing',100,'FontSize',14,'FontWeight','bold','FontSmoothing','on','Interpreter','Latex')
ylabel('$\sigma^{(\textbf{I})}$ (S/m)','Interpreter','Latex')
xlabel('$f$ (MHz)','Interpreter','Latex')
title('$R=2r_0$','Interpreter','Latex','Color',[125/255 30/255 125/255])
ax=gca;
ax.YDir = 'reverse';
ax.YScale = 'log';
ax.YMinorGrid = 'off';
ax.TickLabelInterpreter = 'latex';
xticks([37 46 55])
yticks([0.01 0.1 1 10])
yticklabels({'0.01','0.1','1','10'})
subplot(2,3,5)
[C,h]=contour(f_cst,sig_cst,real(L_30_cst).'*1e9,'LineWidth',2);
h.LevelList = [-1 -0.5 -0.2 -0.05 0.0 0.03 0.04 0.05 0.06 0.08];
clabel(C,h,'LabelSpacing',200,'FontSize',14,'FontWeight','bold','FontSmoothing','on','Interpreter','Latex')
ylabel('$\sigma^{(\textbf{I})}$ (S/m)','Interpreter','Latex')
xlabel('$f$ (MHz)','Interpreter','Latex')
title('$R=3r_0$','Interpreter','Latex','Color',[125/255 30/255 125/255])
ax=gca;
ax.YDir = 'reverse';
ax.YScale = 'log';
ax.YMinorGrid = 'off';
ax.TickLabelInterpreter = 'latex';
xticks([37 46 55])
yticks([0.01 0.1 1 10])
yticklabels({'0.01','0.1','1','10'})
colormap(hsv(1000))
hp4 = get(subplot(2,3,5),'Position');
h = colorbar('Position', [hp4(1)+hp4(3)+0.1 hp4(2) 0.1 hp4(4)*2.2]);
h.TickLabelInterpreter = 'latex';
caxis([-1.8 0.1])
ylabel(h, '$\rm{Re}\{\, \mathcal{L} \,\}$ (nH)','Interpreter','Latex')
set(gcf,'Color','w')
set(findall(gcf,'-property','FontName'),'fontsize',18)
