Z1 = FullSimplify[R1+I*w*L1 + 1/(I*w*C1)]

a1=1;
b1=0;
c1=1/Z1;
d1 =1;
S21 =2/(a1+b1/z0+c1*z0+d1);
resultSingleR =FullSimplify[S21-1]

w1 = 1/((C1 L1)^(1/2));
kin1=R1/L1;
kext1 =z0/(2 L1);
A1=((-2 kext1 w)/(+2 kext1 w+2 kin1 w+2 I ((w^2)-(w1^2))));
FullSimplify[resultSingleR -A1]

Z2 = R2+I*w*L2+ 1/(I*w*C2);
a2=1;
b2=0;
c2=1/Z2;
d2=1;
w2 = 1/((C2 L2)^(1/2));
kin2=R2/L2;
kext2 =z0/(2 L2);
Phase =kl;M1 = {{a1,b1},{c1,d1}} ;
w1box = (w^2-w1^2+I 2w kin1 );
w2box = (w^2-w2^2+I 2w kin2 );
M2 = {{Cos[Phase],-I*z0*Sin[Phase]},{-I/z0*Sin[Phase],Cos[Phase]}} ;
M3= {{a2,b2},{c2,d2}};
M = M1. M2.M3;

MatrixForm[M1]
MatrixForm[M2]
MatrixForm[M3]
MatrixForm[M]

a3 = Part[M,1,1];
b3 = Part[M,1,2];
c3 = Part[M,2,1];
d3 = Part[M,2,2];
S12Coupling = FullSimplify[2(a3*d3-b3*c3)/(a3+b3/z0+c3*z0+d3)]
S21Coupling =FullSimplify[2/(a3+b3/z0+c3*z0+d3)]
FullSimplify[S21Coupling-S12Coupling]

S21pi2 = FullSimplify[2/(-2 I+((w z0 (C1+C2+I C1 C2 w (R1+R2+I (L1+L2) w+z0)))/((-1+C1 w (-I R1+L1 w)) (-1+C2 w (-I R2+L2 w)))))-1];
S21pi2cal = ((2+2 I-((w z0 /( L1 L2)( L1 (w1^2-w^2  +I  w kin1+I  2w kext1 )+L2 ( w2^2-w^2  +I  w kin2)))/((w1^2- w^2+I w kin1) (w2^2-w^2 +I  w kin2 ))))/(((w z0 /( L1 L2)( L1 (w1^2-w^2  +I  w kin1+I  2w kext1 )+L2 ( w2^2-w^2  +I  w kin2)))/((w1^2- w^2+I w kin1) (w2^2-w^2 +I  w kin2 )))-2 I));
S21pi2cal2 = ((2+2 I)/(((w z0 /( L1 L2)( L1 (w1^2-w^2  +I  w kin1+I  2w kext1 )+L2 ( w2^2-w^2  +I  w kin2)))/((w1^2- w^2+I w kin1) (w2^2-w^2 +I  w kin2 )))-2 I))-(w z0 (L1 (2 I kext1 w+I kin1 w-(w^2)+(w1^2))+L2 (I kin2 w-(w^2)+(w2^2))))/((L1 L2) (((w z0 (L1 (2 I kext1 w+I kin1 w-(w^2)+(w1^2))+L2 (I kin2 w-(w^2)+(w2^2))))/(L1 L2))-2 I (I kin1 w-(w^2)+(w1^2)) (I kin2 w-(w^2)+(w2^2))));
FullSimplify[S21pi2-S21pi2cal2]